A gradient-based outer approximation solver for convex mixed-integer nonlinear programming (MINLP)
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README.md

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Pavito

Pavito is a mixed-integer convex programming (MICP) solver package written in Julia. MICP problems are convex except for restrictions that some variables take binary or integer values.

Pavito solves MICP problems by constructing sequential polyhedral outer-approximations of the convex feasible set, similar to Bonmin. Pavito accesses state-of-the-art MILP solvers and continuous, derivative-based nonlinear programming (NLP) solvers through the MathProgBase interface.

For algorithms that use a conic solver instead of an NLP solver, use Pajarito. Pajarito is a robust mixed-integer conic solver that can handle such established problem classes as mixed-integer second-order cone programming (MISOCP) and mixed-integer semidefinite programming (MISDP).

Installation

Pavito can be installed through the Julia package manager:

julia> Pkg.add("Pavito")

Usage

There are several convenient ways to model MICPs in Julia and access Pavito:

JuMP Convex.jl MathProgBase
NLP model X X
Conic model X X X

JuMP and Convex.jl are algebraic modeling interfaces, while MathProgBase is a lower-level interface for providing input in raw callback or matrix form. Convex.jl is perhaps the most user-friendly way to provide input in conic form, since it transparently handles conversion of algebraic expressions. JuMP supports general nonlinear smooth functions, e.g. by using @NLconstraint. JuMP also supports conic modeling, but requires cones to be explicitly specified, e.g. by using norm(x) <= t for second-order cone constraints. Pavito may be accessed through MathProgBase from outside Julia by using the experimental cmpb interface which provides a C API to the low-level conic input format. The ConicBenchmarkUtilities package provides utilities to read files in the CBF format.

MIP and continuous solvers

The algorithm implemented by Pavito itself is relatively simple, and most of the hard work is performed by the MILP solver and the NLP solver. The performance of Pavito depends on these two types of solvers.

The mixed-integer solver is specified by using the mip_solver option to PavitoSolver, e.g. PavitoSolver(mip_solver=CplexSolver()). You must first load the Julia package which provides the mixed-integer solver, e.g. using CPLEX. The continuous derivative-based nonlinear solver (e.g. Ipopt or KNITRO) is specified by using the cont_solver option, e.g. PavitoSolver(cont_solver=IpoptSolver()).

MIP and continuous solver parameters must be specified through their corresponding Julia interfaces. For example, to turn off the output of Ipopt solver, use cont_solver=IpoptSolver(print_level=0).

Pavito solver options

The following options can be passed to PavitoSolver() to modify its behavior:

  • log_level::Int Verbosity flag: 0 for quiet, higher for basic solve info
  • timeout::Float64 Time limit for algorithm (in seconds)
  • rel_gap::Float64 Relative optimality gap termination condition
  • mip_solver_drives::Bool Let MILP solver manage convergence ("branch and cut")
  • mip_solver::MathProgBase.AbstractMathProgSolver MILP solver
  • cont_solver::MathProgBase.AbstractMathProgSolver Continuous NLP solver

Pavito is not yet numerically robust and may require tuning of parameters to improve convergence. If the default parameters don't work for you, please let us know. For improved Pavito performance, MILP solver integrality tolerance and feasibility tolerances should typically be tightened, for example to 1e-8.

Bug reports and support

Please report any issues via the Github issue tracker. All types of issues are welcome and encouraged; this includes bug reports, documentation typos, feature requests, etc. The Optimization (Mathematical) category on Discourse is appropriate for general discussion.