KSOPT_mex

This repository contains a Matlab MEX interface for the nonlinear constrained multiobjective optimization algorithm KSOPT by Gregory A. Wrenn.

The repository is based on the KSOPT code from madebr/pyOpt converted from Fortran to C with f2c.

Compiling the interface

The MEX file can be created by invoking

compile.ksopt;

and copies the created MEX file ksopt_optimize.mex* to the root directory.

MEX interface

The interface of ksopt_optimize is similar to fmincon or fminimax from the Optimization Toolbox. The input arguments are:

• fun: objective function to minimize
• x_0: initial value or matrix of initial values or StartPointSet of initial values to start optimization from
• A: matrix of linear inequlity constraints
• b: upper limits for linear inequality constraints
• Aeq: matrix for linear equality constraints
• beq: upper limits for linear equality constraints
• lb: fixed lower bounds on x
• ub: fixed upper bounds on x
• nonlcon: nonlinear inequality and equality constraints
• options: settings for optimization
• varargin: additional arguments for objective function

A description of the input arguments can be found in the Matlab documentation of e.g. fminimax. The argument options is a structure with the following fields

options = struct(...
  'MaxIterations',                1000,...
  'MaxFunctionEvaluations',       1000,...
  'MaxTime',                      60,...
  'ObjectiveLimit',               -1E20,...
  'FiniteDifferenceStepSize',     1E-6,...
  'FiniteDifferenceStepSizeMin',  1E-6,...
  'OptimalityTolerance',          1E-6,...
  'OptimalityToleranceAbs',       1E-6,...
  'RhoIncrement',                 0.01,...
  'RhoMin',                       0.001,...
  'RhoMax',                       0.1,...
  'Display',                      'iter-detailed',...
  'Scale',                        1,...
  'ScaleVector',                  ones(size(x_0)),...
  'SpecifyObjectiveGradient',     true,...
  'SpecifyConstraintGradient',    true...
);

or can be of type optimoptions or optimset.

The function returns:

• x: optimal value
• fval: function value at optimal value
• exitflag: optimization result indicator
• output: structure with information about optimization

Example

a1 = [1, 1];
b1 = [-1, 1];
c1 = [0, -1];
a0 = 2;
b0 = -3;
c0 = 4;
fun = @(x) [a1*x + a0; b1*x + b0; c1*x + c0];
x_0 = [0; 0];
A = [];
b = [];
Aeq = [];
beq = [];
lb = [];
ub = [];
nonlcon = [];
[x, fval, exitflag, output] = ksopt_optimize(fun, x_0, A, b, Aeq, beq, lb, ub, nonlcon)