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<html>
<head>
<title>
FMINCON_PARALLEL - Minimization via FMINCON and the Parallel Computing Toolbox
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
FMINCON_PARALLEL <br> Minimization via FMINCON and the Parallel Computing Toolbox
</h1>
<hr>
<p>
<b>FMINCON_PARALLEL</b>
is a MATLAB program which
demonstrates how the FMINCON function, which is used to find the
constrained minimizer of a function, can use
MATLAB's Parallel Computing Toolbox to perform some calculations in parallel.
</p>
<p>
The program transcribes a (class of) optimal control problem(s) to finite-dimensional
nonlinear programming problems and then invokes the Matlab solver fmincon.
The problem has a fixed initial state, a fixed terminal time, a Mayer cost
functional and a scalar-valued control function. Data for a specific problem
are supplied by the user; <i>zermelo.m</i> is an example based on efficient
navigation of a boat in a spatially varying current.
</p>
<h3 align = "center">
Usage:
</h3>
<p>
<blockquote>
<b>run_opt</b> ( <i>'function_file'</i>, <i>intervals</i> )
</blockquote>
where
<ul>
<li>
<i>'function_file'</i> is a string that identifies a user supplied
function that returns a data structure with the problem specification
(see the example <i>zermelo.m</i>).
</li>
<li>
<i>intervals</i> is a positive integer that specifies a number of
uniform intervals of the time axis interval [ 0, PAR.tf].
</li>
</ul>
</p>
<p>
The user must supply certain routines:
<ul>
<li>
PAR.rhs, for evaluating the dynamics;
</li>
<li>
PAR.cost, for the Mayer cost functional;
</li>
<li>
PAR.eq, PAR.ineq, for any terminal constraints;
</li>
</ul>
as well as PAR.x0, the initial condition for the state.
</p>
<p>
The user may also supply optional routines:
<ul>
<li>
PAR.plot, for plotting;
</li>
<li>
PAR.initial_guess, an initial estimate for the control values;
</li>
<li>
PAR.ub, PAR.lb, bounds for the controls.
</li>
</ul>
</p>
<p>
No error checking is done to ensure that the specified problem data are consistent.
Strange error messages may result from such inconsistency (e.g. the dimension of the
state - the 'size' of the returned output from PAR.rhs - must be same as the 'size'
of PAR.x0, and the same as the 'size' of the input arguments to PAR.cost, PAR.eq,
and PAR.ineq).
</p>
<p>
To run the code with the sample problem, the command might be
<blockquote>
<b>run_opt</b> ( 'zermelo.m', 16 )
</blockquote>
</p>
<p>
To run the code with the sample problem and the Parallel Computing Toolbox,
the command might be
<blockquote>
matlabpool open local 4<br>
<b>run_opt</b> ( 'zermelo.m', 16 )<br>
matlabpool close
</blockquote>
where, in this case, we have only asked for 4 MATLAB workers.
Assuming successful convergence, plots showing the path of the boat in the plane
and a time history of the piecewise constant controlm will be displayed.
<p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files described and made available on this web page
are distributed under
<a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>FMINCON_PARALLEL</b> is available in
<a href = "../../m_src/fmincon_parallel/fmincon_parallel.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../m_src/cell_detection_tasks/cell_detection_tasks.html">
CELL_DETECTION_TASKS</a>,
a MATLAB program which
creates modified versions of a sequence of gray-scale TIF files containing
images of cells; the process of each file is carried out independently,
using the "task" feature of MATLAB's parallel computing toolbox.
</p>
<p>
<a href = "../../m_src/cg_distributed/cg_distributed.html">
CG_DISTRIBUTED</a>,
a MATLAB program which
implements a version of the NAS CG conjugate gradient benchmark,
using distributed memory.
</p>
<p>
<a href = "../../m_src/collatz_parfor/collatz_parfor.html">
COLLATZ_PARFOR</a>,
a MATLAB program which
seeks the maximum Collatz sequence between 1 and N,
running in parallel using MATLAB's "PARFOR" feature.
</p>
<p>
<a href = "../../m_src/contrast_spmd/contrast_spmd.html">
CONTRAST_SPMD</a>,
a MATLAB program which
demonstrates the SPMD parallel programming feature for image operations;
the client reads an image, the workers increase contrast over separate portions, and
the client assembles and displays the results.
</p>
<p>
<a href = "../../m_src/contrast2_spmd/contrast2_spmd.html">
CONTRAST2_SPMD</a>,
a MATLAB program which
demonstrates the SPMD parallel programming feature for image operations;
this improves the contrast_spmd program by allowing the workers to share some
data; this makes it possible to eliminate artificial "seams" in the processed
image.
</p>
<p>
<a href = "../../m_src/fd2d_heat_explicit_spmd/fd2d_heat_explicit_spmd.html">
FD2D_HEAT_EXPLICIT_SPMD</a>,
a MATLAB program which
uses the finite difference method and explicit time stepping
to solve the time dependent heat equation in 2D. A black and white image
is used as the "initial condition". MATLAB's SPMD facility is used to
carry out the computation in parallel.
</p>
<p>
<a href = "../../m_src/image_denoise_spmd/image_denoise_spmd.html">
IMAGE_DENOISE_SPMD</a>,
a MATLAB program which
demonstrates the SPMD parallel programming feature for image operations;
the client reads an image, the workers process portions of it, and
the client assembles and displays the results.
</p>
<p>
<a href = "../../m_src/linear_solve_distributed/linear_solve_distributed.html">
LINEAR_SOLVE_DISTRIBUTED</a>,
a MATLAB program which
solves a linear system <b>A*x=b</b> using MATLAB's <b>spmd</b> facility,
so that the matrix <b>A</b> is "distributed" across multiple MATLAB workers.
</p>
<p>
<a href = "../../m_src/matlab_parallel/matlab_parallel.html">
MATLAB_PARALLEL</a>,
MATLAB programs which
illustrate "local" parallel programming on a single computer
with MATLAB's Parallel Computing Toolbox.
</p>
<p>
<a href = "../../m_src/md_parfor/md_parfor.html">
MD_PARFOR</a>,
a MATLAB program which
carries out a molecular dynamics simulation,
running in parallel using MATLAB's "PARFOR" feature.
</p>
<p>
<a href = "../../m_src/ode_sweep_parfor/ode_sweep_parfor.html">
ODE_SWEEP_PARFOR</a>,
a MATLAB program which
demonstrates how the PARFOR command can be used to parallelize the computation
of a grid of solutions to a parameterized system of ODE's.
</p>
<p>
<a href = "../../m_src/plot_spmd/plot_spmd.html">
PLOT_SPMD</a>,
a MATLAB library which
demonstrates the SPMD parallel programming feature, by having a number
of labs compute parts of a sine plot, which is then displayed by the
client process.
</p>
<p>
<a href = "../../m_src/prime_parfor/prime_parfor.html">
PRIME_PARFOR</a>,
a MATLAB program which
counts the number of primes between 1 and N;
running in parallel using MATLAB's "PARFOR" feature.
</p>
<p>
<a href = "../../m_src/prime_spmd/prime_spmd.html">
PRIME_SPMD</a>,
a MATLAB program which
counts the number of primes between 1 and N;
running in parallel using MATLAB's "SPMD" feature.
</p>
<p>
<a href = "../../m_src/quad_parfor/quad_parfor.html">
QUAD_PARFOR</a>,
a MATLAB program which
estimates an integral using quadrature;
running in parallel using MATLAB's "PARFOR" feature.
</p>
<p>
<a href = "../../m_src/quad_spmd/quad_spmd.html">
QUAD_SPMD</a>,
a MATLAB program which
estimates an integral using quadrature;
running in parallel using MATLAB's "SPMD" feature.
</p>
<p>
<a href = "../../m_src/quad_tasks/quad_tasks.html">
QUAD_TASKS</a>,
a MATLAB program which
estimates an integral using quadrature;
running in parallel using MATLAB's "TASK" feature.
</p>
<p>
<a href = "../../m_src/random_walk_2d_avoid_tasks/random_walk_2d_avoid_tasks.html">
RANDOM_WALK_2D_AVOID_TASKS</a>,
a MATLAB program which
computes many self avoiding random walks in 2D by creating a job which
defines each walk as a task, and then computes these independently
using MATLAB's Parallel Computing Toolbox task computing capability.
</p>
<p>
<a href = "../../m_src/satisfy_parfor/satisfy_parfor.html">
SATISFY_PARFOR</a>,
a MATLAB program which
demonstrates, for a particular circuit, an exhaustive search
for solutions of the circuit satisfiability problem,
running in parallel using MATLAB's "PARFOR" feature.
</p>
<p>
<a href = "../../m_src/subset_sum_tasks/subset_sum_tasks.html">
SUBSET_SUM_TASKS</a>,
a MATLAB program which
solves a subset sum problem by exhaustive search,
subdividing the search range among separate tasks.
</p>
<h3 align = "center">
Author:
</h3>
<p>
Gene Cliff, <br>
Aerospace and Ocean Engineering / Interdisciplinary Center for Applied Mathematics,<br>
Virginia Tech.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
The User's Guide for the Parallel Computing Toolbox is available at
<a href = "http://www.mathworks.com/access/helpdesk/help/pdf_doc/distcomp/distcomp.pdf">
http://www.mathworks.com/access/helpdesk/help/pdf_doc/distcomp/distcomp.pdf</a>
</p>
<p>
<ul>
<li>
Gaurav Sharma, Jos Martin,<br>
MATLAB: A Language for Parallel Computing,<br>
International Journal of Parallel Programming,<br>
Volume 37, Number 1, pages 3-36, February 2009.
</li>
</ul>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "opt_fun.m">opt_fun.m</a>,
a MATLAB function which accepts the name of a parameter setting function
F_NAME and a discretization parameter N, and calls FMINCON.
</li>
<li>
<a href = "opt_script.m">opt_script.m</a>,
a MATLAB script which runs OPT_FUN with particular arguments.
</li>
<li>
<a href = "opt_pool.m">opt_pool.m</a>,
a script which runs OPT_FUN interactively with 4 MATLAB workers.
</li>
<li>
<a href = "opt_batch_local.m">opt_batch_local.m</a>,
runs OPT_SCRIPT locally using 4 MATLAB workers.
</li>
<li>
<a href = "opt_batch_ithaca.m">opt_batch_ithaca.m</a>,
runs OPT_SCRIPT on the Ithaca cluster using 4 MATLAB workers.
</li>
<li>
<a href = "general_constraint.m">general_constraint.m</a>
evaluates a general constraint.
</li>
<li>
<a href = "general_cost.m">general_cost.m</a>
evaluates a general cost.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<b>ZERMELO</b> is an example problem describing the efficient navigation
of a boat in a spatially varying current. The name "zermelo" is to be used
for the F_NAME parameter of RUN_OPT.
<ul>
<li>
<a href = "zermelo.m">zermelo.m</a>
defines initial data for the problem.
</li>
<li>
<a href = "zermelo_cost.m">zermelo_cost.m</a>
evaluates the cost function.
</li>
<li>
<a href = "zermelo_ineq.m">zermelo_ineq.m</a>
evaluates terminal constraints.
</li>
<li>
<a href = "zermelo_plot.m">zermelo_plot.m</a>
a plotting function.
</li>
<li>
<a href = "zermelo_rhs.m">zermelo_rhs.m</a>
evaluates the dynamics.
</li>
</ul>
</p>
<p>
<ul>
<li>
<a href = "control.png">control.png</a>, a plot of the control;
</li>
<li>
<a href = "opt_output.txt">opt_output.txt</a>
is the output from a run in which the local matlabpool is used
with 4 workers to execute the command "run_opt ( 'zermelo', 16 )".
</li>
<li>
<a href = "path.png">path.png</a>, a plot of the boat's path;
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../m_src.html">
the MATLAB source codes</a>.
</p>
<hr>
<i>
Last revised on 31 March 2010.
</i>
<!-- John Burkardt -->
</body>
</html>