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Joris Gillis edited this page Apr 4, 2023 · 3 revisions

Standard documentation for conic:

 [INTERNAL]

::

 conic(str name, str solver, dict:Sparsity qp, dict opts) -> Function

Create a QP solver Solves the following strictly convex problem:

::

 min          1/2 x' H x + g' x
 x

 subject to
 LBA <= A x <= UBA
 LBX <= x   <= UBX

 resize(Q x, np, np) + P >= 0 (psd)

 with :
 H sparse (n x n) positive definite
 g dense  (n x 1)
 A sparse (nc x n)
 Q sparse symmetric (np^2 x n)
 P sparse symmetric (np x nq)

 n: number of decision variables (x)
 nc: number of constraints (A)
 nq: shape of psd constraint matrix

If H is not positive-definite, the solver should throw an error.

Second-order cone constraints can be added as psd constraints through a helper function 'soc':

x in R^n y in R

|| x ||_2 <= y

<=>

soc(x, y) psd

This can be proven with soc(x, y)=[y*I x; x' y] using the Shur complement.

General information

List of available options

+------------------+-----------------+------------------+------------------+ | Id | Type | Description | Used in | +==================+=================+==================+==================+ | ad_weight | OT_DOUBLE | Weighting factor | casadi::Function | | | | for derivative | Internal | | | | calculation.When | | | | | there is an | | | | | option of either | | | | | using forward or | | | | | reverse mode | | | | | directional | | | | | derivatives, the | | | | | condition ad_wei | | | | | ght*nf<=(1- | | | | | ad_weight)*na is | | | | | used where nf | | | | | and na are | | | | | estimates of the | | | | | number of | | | | | forward/reverse | | | | | mode directional | | | | | derivatives | | | | | needed. By | | | | | default, | | | | | ad_weight is | | | | | calculated | | | | | automatically, | | | | | but this can be | | | | | overridden by | | | | | setting this | | | | | option. In | | | | | particular, 0 | | | | | means forcing | | | | | forward mode and | | | | | 1 forcing | | | | | reverse mode. | | | | | Leave unset for | | | | | (class specific) | | | | | heuristics. | | +------------------+-----------------+------------------+------------------+ | ad_weight_sp | OT_DOUBLE | Weighting factor | casadi::Function | | | | for sparsity | Internal | | | | pattern | | | | | calculation calc | | | | | ulation.Override | | | | | s default | | | | | behavior. Set to | | | | | 0 and 1 to force | | | | | forward and | | | | | reverse mode | | | | | respectively. | | | | | Cf. option | | | | | "ad_weight". | | | | | When set to -1, | | | | | sparsity is | | | | | completely | | | | | ignored and | | | | | dense matrices | | | | | are used. | | +------------------+-----------------+------------------+------------------+ | always_inline | OT_BOOL | Force inlining. | casadi::Function | | | | | Internal | +------------------+-----------------+------------------+------------------+ | cache | OT_DICT | Prepopulate the | casadi::Function | | | | function cache. | Internal | | | | Default: empty | | +------------------+-----------------+------------------+------------------+ | compiler | OT_STRING | Just-in-time | casadi::Function | | | | compiler plugin | Internal | | | | to be used. | | +------------------+-----------------+------------------+------------------+ | custom_jacobian | OT_FUNCTION | Override | casadi::Function | | | | CasADi's AD. Use | Internal | | | | together with | | | | | 'jac_penalty': | | | | | 0. Note: Highly | | | | | experimental. | | | | | Syntax may break | | | | | often. | | +------------------+-----------------+------------------+------------------+ | der_options | OT_DICT | Default options | casadi::Function | | | | to be used to | Internal | | | | populate | | | | | forward_options, | | | | | reverse_options, | | | | | and | | | | | jacobian_options | | | | | before those | | | | | options are | | | | | merged in. | | +------------------+-----------------+------------------+------------------+ | derivative_of | OT_FUNCTION | The function is | casadi::Function | | | | a derivative of | Internal | | | | another | | | | | function. The | | | | | type of | | | | | derivative | | | | | (directional | | | | | derivative, | | | | | Jacobian) is | | | | | inferred from | | | | | the function | | | | | name. | | +------------------+-----------------+------------------+------------------+ | discrete | OT_BOOLVECTOR | Indicates which | casadi::Conic | | | | of the variables | | | | | are discrete, | | | | | i.e. integer- | | | | | valued | | +------------------+-----------------+------------------+------------------+ | dump | OT_BOOL | Dump function to | casadi::Function | | | | file upon first | Internal | | | | evaluation. | | | | | [false] | | +------------------+-----------------+------------------+------------------+ | dump_dir | OT_STRING | Directory to | casadi::Function | | | | dump | Internal | | | | inputs/outputs | | | | | to. Make sure | | | | | the directory | | | | | exists [.] | | +------------------+-----------------+------------------+------------------+ | dump_format | OT_STRING | Choose file | casadi::Function | | | | format to dump | Internal | | | | matrices. See | | | | | DM.from_file | | | | | [mtx] | | +------------------+-----------------+------------------+------------------+ | dump_in | OT_BOOL | Dump numerical | casadi::Function | | | | values of inputs | Internal | | | | to file | | | | | (readable with | | | | | DM.from_file ) | | | | | [default: false] | | +------------------+-----------------+------------------+------------------+ | dump_out | OT_BOOL | Dump numerical | casadi::Function | | | | values of | Internal | | | | outputs to file | | | | | (readable with | | | | | DM.from_file ) | | | | | [default: false] | | +------------------+-----------------+------------------+------------------+ | enable_fd | OT_BOOL | Enable | casadi::Function | | | | derivative | Internal | | | | calculation by | | | | | finite | | | | | differencing. | | | | | [default: | | | | | false]] | | +------------------+-----------------+------------------+------------------+ | enable_forward | OT_BOOL | Enable | casadi::Function | | | | derivative | Internal | | | | calculation | | | | | using generated | | | | | functions for | | | | | Jacobian-times- | | | | | vector products | | | | | - typically | | | | | using forward | | | | | mode AD - if | | | | | available. | | | | | [default: true] | | +------------------+-----------------+------------------+------------------+ | enable_jacobian | OT_BOOL | Enable | casadi::Function | | | | derivative | Internal | | | | calculation | | | | | using generated | | | | | functions for | | | | | Jacobians of all | | | | | differentiable | | | | | outputs with | | | | | respect to all | | | | | differentiable | | | | | inputs - if | | | | | available. | | | | | [default: true] | | +------------------+-----------------+------------------+------------------+ | enable_reverse | OT_BOOL | Enable | casadi::Function | | | | derivative | Internal | | | | calculation | | | | | using generated | | | | | functions for | | | | | transposed | | | | | Jacobian-times- | | | | | vector products | | | | | - typically | | | | | using reverse | | | | | mode AD - if | | | | | available. | | | | | [default: true] | | +------------------+-----------------+------------------+------------------+ | error_on_fail | OT_BOOL | Throw exceptions | casadi::ProtoFun | | | | when function | ction | | | | evaluation fails | | | | | (default true). | | +------------------+-----------------+------------------+------------------+ | fd_method | OT_STRING | Method for | casadi::Function | | | | finite | Internal | | | | differencing | | | | | [default | | | | | 'central'] | | +------------------+-----------------+------------------+------------------+ | fd_options | OT_DICT | Options to be | casadi::Function | | | | passed to the | Internal | | | | finite | | | | | difference | | | | | instance | | +------------------+-----------------+------------------+------------------+ | forward_options | OT_DICT | Options to be | casadi::Function | | | | passed to a | Internal | | | | forward mode | | | | | constructor | | +------------------+-----------------+------------------+------------------+ | gather_stats | OT_BOOL | Deprecated | casadi::Function | | | | option | Internal | | | | (ignored): | | | | | Statistics are | | | | | now always | | | | | collected. | | +------------------+-----------------+------------------+------------------+ | input_scheme | OT_STRINGVECTOR | Deprecated | casadi::Function | | | | option (ignored) | Internal | +------------------+-----------------+------------------+------------------+ | inputs_check | OT_BOOL | Throw exceptions | casadi::Function | | | | when the | Internal | | | | numerical values | | | | | of the inputs | | | | | don't make sense | | +------------------+-----------------+------------------+------------------+ | is_diff_in | OT_BOOLVECTOR | Indicate for | casadi::Function | | | | each input if it | Internal | | | | should be | | | | | differentiable. | | +------------------+-----------------+------------------+------------------+ | is_diff_out | OT_BOOLVECTOR | Indicate for | casadi::Function | | | | each output if | Internal | | | | it should be | | | | | differentiable. | | +------------------+-----------------+------------------+------------------+ | jac_penalty | OT_DOUBLE | When requested | casadi::Function | | | | for a number of | Internal | | | | forward/reverse | | | | | directions, it | | | | | may be cheaper | | | | | to compute first | | | | | the full | | | | | jacobian and | | | | | then multiply | | | | | with seeds, | | | | | rather than | | | | | obtain the | | | | | requested | | | | | directions in a | | | | | straightforward | | | | | manner. Casadi | | | | | uses a heuristic | | | | | to decide which | | | | | is cheaper. A | | | | | high value of | | | | | 'jac_penalty' | | | | | makes it less | | | | | likely for the | | | | | heurstic to | | | | | chose the full | | | | | Jacobian | | | | | strategy. The | | | | | special value -1 | | | | | indicates never | | | | | to use the full | | | | | Jacobian | | | | | strategy | | +------------------+-----------------+------------------+------------------+ | jacobian_options | OT_DICT | Options to be | casadi::Function | | | | passed to a | Internal | | | | Jacobian | | | | | constructor | | +------------------+-----------------+------------------+------------------+ | jit | OT_BOOL | Use just-in-time | casadi::Function | | | | compiler to | Internal | | | | speed up the | | | | | evaluation | | +------------------+-----------------+------------------+------------------+ | jit_cleanup | OT_BOOL | Cleanup up the | casadi::Function | | | | temporary source | Internal | | | | file that jit | | | | | creates. | | | | | Default: true | | +------------------+-----------------+------------------+------------------+ | jit_name | OT_STRING | The file name | casadi::Function | | | | used to write | Internal | | | | out code. The | | | | | actual file | | | | | names used | | | | | depend on 'jit_t | | | | | emp_suffix' and | | | | | include | | | | | extensions. | | | | | Default: | | | | | 'jit_tmp' | | +------------------+-----------------+------------------+------------------+ | jit_options | OT_DICT | Options to be | casadi::Function | | | | passed to the | Internal | | | | jit compiler. | | +------------------+-----------------+------------------+------------------+ | jit_serialize | OT_STRING | Specify | casadi::Function | | | | behaviour when | Internal | | | | serializing a | | | | | jitted function: | | | | | SOURCE|link|embe | | | | | d. | | +------------------+-----------------+------------------+------------------+ | jit_temp_suffix | OT_BOOL | Use a temporary | casadi::Function | | | | (seemingly | Internal | | | | random) filename | | | | | suffix for | | | | | generated code | | | | | and libraries. | | | | | This is desired | | | | | for thread- | | | | | safety. This | | | | | behaviour may | | | | | defeat caching | | | | | compiler | | | | | wrappers. | | | | | Default: true | | +------------------+-----------------+------------------+------------------+ | max_io | OT_INT | Acceptable | casadi::Function | | | | number of inputs | Internal | | | | and outputs. | | | | | Warn if | | | | | exceeded. | | +------------------+-----------------+------------------+------------------+ | max_num_dir | OT_INT | Specify the | casadi::Function | | | | maximum number | Internal | | | | of directions | | | | | for derivative | | | | | functions. | | | | | Overrules the | | | | | builtin optimize | | | | | d_num_dir. | | +------------------+-----------------+------------------+------------------+ | never_inline | OT_BOOL | Forbid inlining. | casadi::Function | | | | | Internal | +------------------+-----------------+------------------+------------------+ | output_scheme | OT_STRINGVECTOR | Deprecated | casadi::Function | | | | option (ignored) | Internal | +------------------+-----------------+------------------+------------------+ | post_expand | OT_BOOL | After | casadi::Function | | | | construction, | Internal | | | | expand this | | | | | Function . | | | | | Default: False | | +------------------+-----------------+------------------+------------------+ | post_expand_opti | OT_DICT | Options to be | casadi::Function | | ons | | passed to post- | Internal | | | | construction | | | | | expansion. | | | | | Default: empty | | +------------------+-----------------+------------------+------------------+ | print_in | OT_BOOL | Print numerical | casadi::Function | | | | values of inputs | Internal | | | | [default: false] | | +------------------+-----------------+------------------+------------------+ | print_out | OT_BOOL | Print numerical | casadi::Function | | | | values of | Internal | | | | outputs | | | | | [default: false] | | +------------------+-----------------+------------------+------------------+ | print_problem | OT_BOOL | Print a numeric | casadi::Conic | | | | description of | | | | | the problem | | +------------------+-----------------+------------------+------------------+ | print_time | OT_BOOL | print | casadi::ProtoFun | | | | information | ction | | | | about execution | | | | | time. Implies | | | | | record_time. | | +------------------+-----------------+------------------+------------------+ | record_time | OT_BOOL | record | casadi::ProtoFun | | | | information | ction | | | | about execution | | | | | time, for | | | | | retrieval with | | | | | stats(). | | +------------------+-----------------+------------------+------------------+ | regularity_check | OT_BOOL | Throw exceptions | casadi::ProtoFun | | | | when NaN or Inf | ction | | | | appears during | | | | | evaluation | | +------------------+-----------------+------------------+------------------+ | reverse_options | OT_DICT | Options to be | casadi::Function | | | | passed to a | Internal | | | | reverse mode | | | | | constructor | | +------------------+-----------------+------------------+------------------+ | user_data | OT_VOIDPTR | A user-defined | casadi::Function | | | | field that can | Internal | | | | be used to | | | | | identify the | | | | | function or pass | | | | | additional | | | | | information | | +------------------+-----------------+------------------+------------------+ | verbose | OT_BOOL | Verbose | casadi::ProtoFun | | | | evaluation for | ction | | | | debugging | | +------------------+-----------------+------------------+------------------+

Input scheme: casadi::ConicInput (CONIC_NUM_IN = 12)

+--------------+--------+--------------------------------------------------+ | Full name | Short | Description | +==============+========+==================================================+ | CONIC_H | h | The square matrix H: sparse, (n x n). Only the | | | | lower triangular part is actually used. The | | | | matrix is assumed to be symmetrical. | +--------------+--------+--------------------------------------------------+ | CONIC_G | g | The vector g: dense, (n x 1) | +--------------+--------+--------------------------------------------------+ | CONIC_A | a | The matrix A: sparse, (nc x n) - product with x | | | | must be dense. | +--------------+--------+--------------------------------------------------+ | CONIC_LBA | lba | dense, (nc x 1) | +--------------+--------+--------------------------------------------------+ | CONIC_UBA | uba | dense, (nc x 1) | +--------------+--------+--------------------------------------------------+ | CONIC_LBX | lbx | dense, (n x 1) | +--------------+--------+--------------------------------------------------+ | CONIC_UBX | ubx | dense, (n x 1) | +--------------+--------+--------------------------------------------------+ | CONIC_X0 | x0 | dense, (n x 1) | +--------------+--------+--------------------------------------------------+ | CONIC_LAM_X0 | lam_x0 | dense | +--------------+--------+--------------------------------------------------+ | CONIC_LAM_A0 | lam_a0 | dense | +--------------+--------+--------------------------------------------------+ | CONIC_Q | q | The matrix Q: sparse symmetric, (np^2 x n) | +--------------+--------+--------------------------------------------------+ | CONIC_P | p | The matrix P: sparse symmetric, (np x np) | +--------------+--------+--------------------------------------------------+

Output scheme: casadi::ConicOutput (CONIC_NUM_OUT = 4)

+-------------+-------+---------------------------------------------------+ | Full name | Short | Description | +=============+=======+===================================================+ | CONIC_X | x | The primal solution. | +-------------+-------+---------------------------------------------------+ | CONIC_COST | cost | The optimal cost. | +-------------+-------+---------------------------------------------------+ | CONIC_LAM_A | lam_a | The dual solution corresponding to linear bounds. | +-------------+-------+---------------------------------------------------+ | CONIC_LAM_X | lam_x | The dual solution corresponding to simple bounds. | +-------------+-------+---------------------------------------------------+

List of plugins

  • cbc

  • clp

  • cplex

  • ecos

  • gurobi

  • highs

  • hpipm

  • hpmpc

  • mosek

  • ooqp

  • osqp

  • proxqp

  • qpalm

  • qpoases

  • sqic

  • superscs

  • ipqp

  • nlpsol

  • qrqp

Note: some of the plugins in this list might not be available on your

system. Also, there might be extra plugins available to you that are not listed here. You can obtain their documentation with
Conic.doc("myextraplugin")

cbc

Interface to Cbc solver for sparse Quadratic Programs

Extra doc: https://github.com/casadi/casadi/wiki/L_221

List of available options

+-------------+-----------------------+------------------------------------+ | Id | Type | Description | +=============+=======================+====================================+ | cbc | OT_DICT | Options to be passed to CBC.Three | | | | sets of options are supported. The | | | | first can be found in | | | | OsiSolverParameters.hpp. The | | | | second can be found in | | | | CbcModel.hpp. The third are | | | | options that can be passed to | | | | CbcMain1. | +-------------+-----------------------+------------------------------------+ | hot_start | OT_BOOL | Hot start with x0 [Default false]. | +-------------+-----------------------+------------------------------------+ | sos_groups | OT_INTVECTORVECTOR | Definition of SOS groups by | | | | indices. | +-------------+-----------------------+------------------------------------+ | sos_types | OT_INTVECTOR | Specify 1 or 2 for each SOS group. | +-------------+-----------------------+------------------------------------+ | sos_weights | OT_DOUBLEVECTORVECTOR | Weights corresponding to SOS | | | | entries. | +-------------+-----------------------+------------------------------------+

clp

Interface to Clp solver for sparse Quadratic Programs

Extra doc: https://github.com/casadi/casadi/wiki/L_22d

List of available options

+-----+---------+----------------------------------------------------------+ | Id | Type | Description | +=====+=========+==========================================================+ | clp | OT_DICT | Options to be passed to CLP. A first set of options can | | | | be found in ClpParameters.hpp. eg. 'PrimalTolerance'. | | | | There are other options in additions. 'AutomaticScaling' | | | | (bool) is recognised. 'initial_solve' (default off) | | | | activates the use of Clp's initialSolve. | | | | 'initial_solve_options' takes a dictionary with | | | | following keys (see ClpSolve.hpp): SolveType (string), | | | | PresolveType (string), NumberPasses, SpecialOptions | | | | (intvectorvector), IndependentOptions (intvectorvector). | +-----+---------+----------------------------------------------------------+

cplex

Interface to Cplex solver for sparse Quadratic Programs

Extra doc: https://github.com/casadi/casadi/wiki/L_22a

List of available options

+----------------+-----------------------+---------------------------------+ | Id | Type | Description | +================+=======================+=================================+ | cplex | OT_DICT | Options to be passed to CPLEX | +----------------+-----------------------+---------------------------------+ | dep_check | OT_INT | Detect redundant constraints. | +----------------+-----------------------+---------------------------------+ | dump_filename | OT_STRING | The filename to dump to. | +----------------+-----------------------+---------------------------------+ | dump_to_file | OT_BOOL | Dumps QP to file in CPLEX | | | | format. | +----------------+-----------------------+---------------------------------+ | mip_start | OT_BOOL | Hot start integers with x0 | | | | [Default false]. | +----------------+-----------------------+---------------------------------+ | qp_method | OT_INT | Determines which CPLEX | | | | algorithm to use. | +----------------+-----------------------+---------------------------------+ | sos_groups | OT_INTVECTORVECTOR | Definition of SOS groups by | | | | indices. | +----------------+-----------------------+---------------------------------+ | sos_types | OT_INTVECTOR | Specify 1 or 2 for each SOS | | | | group. | +----------------+-----------------------+---------------------------------+ | sos_weights | OT_DOUBLEVECTORVECTOR | Weights corresponding to SOS | | | | entries. | +----------------+-----------------------+---------------------------------+ | tol | OT_DOUBLE | Tolerance of solver | +----------------+-----------------------+---------------------------------+ | version_suffix | OT_STRING | Specify version of cplex to | | | | load. We will attempt to load l | | | | ibcplex<version_suffix>.[so|dll | | | | |dylib]. Default value is taken | | | | from CPLEX_VERSION env | | | | variable. | +----------------+-----------------------+---------------------------------+ | warm_start | OT_BOOL | Use warm start with simplex | | | | methods (affects only the | | | | simplex methods). | +----------------+-----------------------+---------------------------------+

ecos

Interface to the ECOS Solver for quadratic programming

Extra doc: https://github.com/casadi/casadi/wiki/L_22e

List of available options

+-------+-----------------+------------------------------------------------+ | Id | Type | Description | +=======+=================+================================================+ | ecos | OT_DICT | Options to be passed to ecos. | +-------+-----------------+------------------------------------------------+ | vtype | OT_STRINGVECTOR | Type of variables: | | | | [CONTINUOUS|binary|integer|semicont|semiint] | +-------+-----------------+------------------------------------------------+

gurobi

Interface to the GUROBI Solver for quadratic programming

Extra doc: https://github.com/casadi/casadi/wiki/L_22q

List of available options

+-------------+-----------------------+------------------------------------+ | Id | Type | Description | +=============+=======================+====================================+ | gurobi | OT_DICT | Options to be passed to gurobi. | +-------------+-----------------------+------------------------------------+ | sos_groups | OT_INTVECTORVECTOR | Definition of SOS groups by | | | | indices. | +-------------+-----------------------+------------------------------------+ | sos_types | OT_INTVECTOR | Specify 1 or 2 for each SOS group. | +-------------+-----------------------+------------------------------------+ | sos_weights | OT_DOUBLEVECTORVECTOR | Weights corresponding to SOS | | | | entries. | +-------------+-----------------------+------------------------------------+ | vtype | OT_STRINGVECTOR | Type of variables: [CONTINUOUS|bin | | | | ary|integer|semicont|semiint] | +-------------+-----------------------+------------------------------------+

highs

Interface to HiGHS solver for sparse Quadratic Programs, see highs.dev for more information and https://www.maths.ed.ac.uk/hall/HiGHS/HighsOptions.html for a list of options.

Extra doc: https://github.com/casadi/casadi/wiki/L_22f

List of available options

+-------+---------+--------------------------------+ | Id | Type | Description | +=======+=========+================================+ | highs | OT_DICT | Options to be passed to HiGHS. | +-------+---------+--------------------------------+

hpipm

Interface to HMPC Solver

In order to use this interface, you must:

Decision variables must only by state and control, and the variable

ordering must be [x0 u0 x1 u1 ...]

The constraints must be in order: [ gap0 lincon0 gap1 lincon1 ]

gap: Ak+1 = Ak xk + Bk uk lincon: yk= Ck xk + Dk uk

::

        A0 B0 -I
        C0 D0
               A1 B1 -I
               C1 D1

where I must be a diagonal sparse matrix Either supply all of N, nx, ng, nu options or rely on automatic detection

Extra doc: https://github.com/casadi/casadi/wiki/L_242

List of available options

+-------+--------------+--------------------------------------------------+ | Id | Type | Description | +=======+==============+==================================================+ | N | OT_INT | OCP horizon | +-------+--------------+--------------------------------------------------+ | hpipm | OT_DICT | Options to be passed to hpipm | +-------+--------------+--------------------------------------------------+ | inf | OT_DOUBLE | Replace infinities by this amount [default: 1e8] | +-------+--------------+--------------------------------------------------+ | ng | OT_INTVECTOR | Number of non-dynamic constraints, length N+1 | +-------+--------------+--------------------------------------------------+ | nu | OT_INTVECTOR | Number of controls, length N | +-------+--------------+--------------------------------------------------+ | nx | OT_INTVECTOR | Number of states, length N+1 | +-------+--------------+--------------------------------------------------+

hpmpc

Interface to HMPC Solver

In order to use this interface, you must:

Decision variables must only by state and control, and the variable

ordering must be [x0 u0 x1 u1 ...]

The constraints must be in order: [ gap0 lincon0 gap1 lincon1 ]

gap: Ak+1 = Ak xk + Bk uk lincon: yk= Ck xk + Dk uk

::

        A0 B0 -I
        C0 D0
               A1 B1 -I
               C1 D1

where I must be a diagonal sparse matrix Either supply all of N, nx, ng, nu options or rely on automatic detection

Extra doc: https://github.com/casadi/casadi/wiki/L_22p

List of available options

+----------------+--------------+------------------------------------------+ | Id | Type | Description | +================+==============+==========================================+ | N | OT_INT | OCP horizon | +----------------+--------------+------------------------------------------+ | blasfeo_target | OT_STRING | hpmpc target | +----------------+--------------+------------------------------------------+ | inf | OT_DOUBLE | HPMPC cannot handle infinities. | | | | Infinities will be replaced by this | | | | option's value. | +----------------+--------------+------------------------------------------+ | max_iter | OT_INT | Max number of iterations | +----------------+--------------+------------------------------------------+ | mu0 | OT_DOUBLE | Max element in cost function as estimate | | | | of max multiplier | +----------------+--------------+------------------------------------------+ | ng | OT_INTVECTOR | Number of non-dynamic constraints, | | | | length N+1 | +----------------+--------------+------------------------------------------+ | nu | OT_INTVECTOR | Number of controls, length N | +----------------+--------------+------------------------------------------+ | nx | OT_INTVECTOR | Number of states, length N+1 | +----------------+--------------+------------------------------------------+ | print_level | OT_INT | Amount of diagnostic printing [Default: | | | | 1]. | +----------------+--------------+------------------------------------------+ | target | OT_STRING | hpmpc target | +----------------+--------------+------------------------------------------+ | tol | OT_DOUBLE | Tolerance in the duality measure | +----------------+--------------+------------------------------------------+ | warm_start | OT_BOOL | Use warm-starting | +----------------+--------------+------------------------------------------+

mosek

Interface to the MOSEK Solver for quadratic programming

Extra doc: https://github.com/casadi/casadi/wiki/L_21x

List of available options

+-------+-----------------+------------------------------------------------+ | Id | Type | Description | +=======+=================+================================================+ | mosek | OT_DICT | Options to be passed to mosek. | +-------+-----------------+------------------------------------------------+ | vtype | OT_STRINGVECTOR | Type of variables: | | | | [CONTINUOUS|binary|integer|semicont|semiint] | +-------+-----------------+------------------------------------------------+

ooqp

Interface to the OOQP Solver for quadratic programming The current

implementation assumes that OOQP is configured with the MA27 sparse linear solver.

NOTE: when doing multiple calls to evaluate(), check if you need to

reInit();

Extra doc: https://github.com/casadi/casadi/wiki/L_222

List of available options

+-------------+-----------+------------------------------------------------+ | Id | Type | Description | +=============+===========+================================================+ | artol | OT_DOUBLE | tolerance as provided with setArTol to OOQP | +-------------+-----------+------------------------------------------------+ | mutol | OT_DOUBLE | tolerance as provided with setMuTol to OOQP | +-------------+-----------+------------------------------------------------+ | print_level | OT_INT | Print level. OOQP listens to print_level 0, 10 | | | | and 100 | +-------------+-----------+------------------------------------------------+

osqp

Interface to the OSQP Solver for quadratic programming

Extra doc: https://github.com/casadi/casadi/wiki/L_220

Interface to the PROXQP Solver for quadratic programming

Extra doc: https://github.com/casadi/casadi/wiki/L_243

List of available options

+-------------------+---------+--------------------------------------------+ | Id | Type | Description | +===================+=========+============================================+ | osqp | OT_DICT | const Options to be passed to osqp. | +-------------------+---------+--------------------------------------------+ | warm_start_dual | OT_BOOL | Use lam_a0 and lam_x0 input to warmstart | | | | [Default: truw]. | +-------------------+---------+--------------------------------------------+ | warm_start_primal | OT_BOOL | Use x0 input to warmstart [Default: true]. | +-------------------+---------+--------------------------------------------+

proxqp

List of available options

+-------------------+---------+--------------------------------------------+ | Id | Type | Description | +===================+=========+============================================+ | proxqp | OT_DICT | const proxqp options. | +-------------------+---------+--------------------------------------------+ | warm_start_dual | OT_BOOL | Use y and z input to warmstart [Default: | | | | true]. | +-------------------+---------+--------------------------------------------+ | warm_start_primal | OT_BOOL | Use x input to warmstart [Default: true]. | +-------------------+---------+--------------------------------------------+

qpalm

Interface to the QPALM Solver for quadratic programming

Extra doc: https://github.com/casadi/casadi/wiki/L_22n

List of available options

+-------------------+---------+--------------------------------------------+ | Id | Type | Description | +===================+=========+============================================+ | qpalm | OT_DICT | const Options to be passed to qpalm. | +-------------------+---------+--------------------------------------------+ | warm_start_dual | OT_BOOL | Use lam_a0 and lam_x0 input to warmstart | | | | [Default: true]. | +-------------------+---------+--------------------------------------------+ | warm_start_primal | OT_BOOL | Use x0 input to warmstart [Default: true]. | +-------------------+---------+--------------------------------------------+

qpoases

Interface to QPOases Solver for quadratic programming

::

 Extra doc: https://github.com/casadi/casadi/wiki/L_22o

List of available options

+-------------------------------+-----------+------------------------------+ | Id | Type | Description | +===============================+===========+==============================+ | CPUtime | OT_DOUBLE | The maximum allowed CPU time | | | | in seconds for the whole | | | | initialisation (and the | | | | actually required one on | | | | output). Disabled if unset. | +-------------------------------+-----------+------------------------------+ | boundRelaxation | OT_DOUBLE | Initial relaxation of bounds | | | | to start homotopy and | | | | initial value for far | | | | bounds. | +-------------------------------+-----------+------------------------------+ | boundTolerance | OT_DOUBLE | If upper and lower bounds | | | | differ less than this | | | | tolerance, they are regarded | | | | equal, i.e. as equality | | | | constraint. | +-------------------------------+-----------+------------------------------+ | enableCholeskyRefactorisation | OT_INT | Specifies the frequency of a | | | | full re-factorisation of | | | | projected Hessian matrix: 0: | | | | turns them off, 1: uses them | | | | at each iteration etc. | +-------------------------------+-----------+------------------------------+ | enableDriftCorrection | OT_INT | Specifies the frequency of | | | | drift corrections: 0: turns | | | | them off. | +-------------------------------+-----------+------------------------------+ | enableEqualities | OT_BOOL | Specifies whether equalities | | | | should be treated as always | | | | active (True) or not (False) | +-------------------------------+-----------+------------------------------+ | enableFarBounds | OT_BOOL | Enables the use of far | | | | bounds. | +-------------------------------+-----------+------------------------------+ | enableFlippingBounds | OT_BOOL | Enables the use of flipping | | | | bounds. | +-------------------------------+-----------+------------------------------+ | enableFullLITests | OT_BOOL | Enables condition-hardened | | | | (but more expensive) LI | | | | test. | +-------------------------------+-----------+------------------------------+ | enableInertiaCorrection | OT_BOOL | Should working set be | | | | repaired when negative | | | | curvature is discovered | | | | during hotstart. | +-------------------------------+-----------+------------------------------+ | enableNZCTests | OT_BOOL | Enables nonzero curvature | | | | tests. | +-------------------------------+-----------+------------------------------+ | enableRamping | OT_BOOL | Enables ramping. | +-------------------------------+-----------+------------------------------+ | enableRegularisation | OT_BOOL | Enables automatic Hessian | | | | regularisation. | +-------------------------------+-----------+------------------------------+ | epsDen | OT_DOUBLE | Denominator tolerance for | | | | ratio tests. | +-------------------------------+-----------+------------------------------+ | epsFlipping | OT_DOUBLE | Tolerance of squared | | | | Cholesky diagonal factor | | | | which triggers flipping | | | | bound. | +-------------------------------+-----------+------------------------------+ | epsIterRef | OT_DOUBLE | Early termination tolerance | | | | for iterative refinement. | +-------------------------------+-----------+------------------------------+ | epsLITests | OT_DOUBLE | Tolerance for linear | | | | independence tests. | +-------------------------------+-----------+------------------------------+ | epsNZCTests | OT_DOUBLE | Tolerance for nonzero | | | | curvature tests. | +-------------------------------+-----------+------------------------------+ | epsNum | OT_DOUBLE | Numerator tolerance for | | | | ratio tests. | +-------------------------------+-----------+------------------------------+ | epsRegularisation | OT_DOUBLE | Scaling factor of identity | | | | matrix used for Hessian | | | | regularisation. | +-------------------------------+-----------+------------------------------+ | finalRamping | OT_DOUBLE | Final value for ramping | | | | strategy. | +-------------------------------+-----------+------------------------------+ | growFarBounds | OT_DOUBLE | Factor to grow far bounds. | +-------------------------------+-----------+------------------------------+ | hessian_type | OT_STRING | Type of Hessian - see | | | | qpOASES documentation [UNKNO | | | | WN|posdef|semidef|indef|zero | | | | |identity]] | +-------------------------------+-----------+------------------------------+ | initialFarBounds | OT_DOUBLE | Initial size for far bounds. | +-------------------------------+-----------+------------------------------+ | initialRamping | OT_DOUBLE | Start value for ramping | | | | strategy. | +-------------------------------+-----------+------------------------------+ | initialStatusBounds | OT_STRING | Initial status of bounds at | | | | first iteration. | +-------------------------------+-----------+------------------------------+ | linsol_plugin | OT_STRING | Linear solver plugin | +-------------------------------+-----------+------------------------------+ | maxDualJump | OT_DOUBLE | Maximum allowed jump in dual | | | | variables in linear | | | | independence tests. | +-------------------------------+-----------+------------------------------+ | maxPrimalJump | OT_DOUBLE | Maximum allowed jump in | | | | primal variables in nonzero | | | | curvature tests. | +-------------------------------+-----------+------------------------------+ | max_schur | OT_INT | Maximal number of Schur | | | | updates [75] | +-------------------------------+-----------+------------------------------+ | nWSR | OT_INT | The maximum number of | | | | working set recalculations | | | | to be performed during the | | | | initial homotopy. Default is | | | | 5(nx + nc) | +-------------------------------+-----------+------------------------------+ | numRefinementSteps | OT_INT | Maximum number of iterative | | | | refinement steps. | +-------------------------------+-----------+------------------------------+ | numRegularisationSteps | OT_INT | Maximum number of successive | | | | regularisation steps. | +-------------------------------+-----------+------------------------------+ | printLevel | OT_STRING | Defines the amount of text | | | | output during QP solution, | | | | see Section 5.7 | +-------------------------------+-----------+------------------------------+ | schur | OT_BOOL | Use Schur Complement | | | | Approach [false] | +-------------------------------+-----------+------------------------------+ | sparse | OT_BOOL | Formulate the QP using | | | | sparse matrices. [false] | +-------------------------------+-----------+------------------------------+ | terminationTolerance | OT_DOUBLE | Relative termination | | | | tolerance to stop homotopy. | +-------------------------------+-----------+------------------------------+

sqic

Interface to the SQIC solver for quadratic programming

Extra doc: https://github.com/casadi/casadi/wiki/L_21s

superscs

Interface to the SuperSCS solver for conic programming

Joris Gillis, 2019

Extra doc: https://github.com/casadi/casadi/wiki/L_21z

List of available options

+----------+---------+-----------------------------------+ | Id | Type | Description | +==========+=========+===================================+ | superscs | OT_DICT | Options to be passed to superscs. | +----------+---------+-----------------------------------+

ipqp

Solves QPs using a Mehrotra predictor-corrector interior point method

Extra doc: https://github.com/casadi/casadi/wiki/L_23c

List of available options

+-----------------------+-----------+--------------------------------------+ | Id | Type | Description | +=======================+===========+======================================+ | constr_viol_tol | OT_DOUBLE | Constraint violation tolerance | | | | [1e-8]. | +-----------------------+-----------+--------------------------------------+ | dual_inf_tol | OT_DOUBLE | Dual feasibility violation tolerance | | | | [1e-8] | +-----------------------+-----------+--------------------------------------+ | linear_solver | OT_STRING | A custom linear solver creator | | | | function [default: ldl] | +-----------------------+-----------+--------------------------------------+ | linear_solver_options | OT_DICT | Options to be passed to the linear | | | | solver | +-----------------------+-----------+--------------------------------------+ | max_iter | OT_INT | Maximum number of iterations [1000]. | +-----------------------+-----------+--------------------------------------+ | min_lam | OT_DOUBLE | Smallest multiplier treated as | | | | inactive for the initial active set | | | | [0]. | +-----------------------+-----------+--------------------------------------+ | print_header | OT_BOOL | Print header [true]. | +-----------------------+-----------+--------------------------------------+ | print_info | OT_BOOL | Print info [true]. | +-----------------------+-----------+--------------------------------------+ | print_iter | OT_BOOL | Print iterations [true]. | +-----------------------+-----------+--------------------------------------+

nlpsol

Solve QPs using an Nlpsol Use the 'nlpsol' option to specify the NLP solver to use.

Extra doc: https://github.com/casadi/casadi/wiki/L_235

List of available options

+----------------+-----------+---------------------------------+ | Id | Type | Description | +================+===========+=================================+ | nlpsol | OT_STRING | Name of solver. | +----------------+-----------+---------------------------------+ | nlpsol_options | OT_DICT | Options to be passed to solver. | +----------------+-----------+---------------------------------+

qrqp

Solve QPs using an active-set method

Extra doc: https://github.com/casadi/casadi/wiki/L_22y

List of available options

+-----------------+-----------+--------------------------------------------+ | Id | Type | Description | +=================+===========+============================================+ | constr_viol_tol | OT_DOUBLE | Constraint violation tolerance [1e-8]. | +-----------------+-----------+--------------------------------------------+ | dual_inf_tol | OT_DOUBLE | Dual feasibility violation tolerance | | | | [1e-8] | +-----------------+-----------+--------------------------------------------+ | max_iter | OT_INT | Maximum number of iterations [1000]. | +-----------------+-----------+--------------------------------------------+ | min_lam | OT_DOUBLE | Smallest multiplier treated as inactive | | | | for the initial active set [0]. | +-----------------+-----------+--------------------------------------------+ | print_header | OT_BOOL | Print header [true]. | +-----------------+-----------+--------------------------------------------+ | print_info | OT_BOOL | Print info [true]. | +-----------------+-----------+--------------------------------------------+ | print_iter | OT_BOOL | Print iterations [true]. | +-----------------+-----------+--------------------------------------------+ | print_lincomb | OT_BOOL | Print dependant linear combinations of | | | | constraints [false]. Printed numbers are | | | | 0-based indices into the vector of [simple | | | | bounds;linear bounds] | +-----------------+-----------+--------------------------------------------+

Joel Andersson

Extra doc: https://github.com/casadi/casadi/wiki/L_21n

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/conic.hpp#L43

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/conic.cpp#L43-L46

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