memoize-fmincon

Memoized version of fmincon with MATLAB

The fmincon function takes as input the objective and constraints functions as separate inputs; as such, if an expensive comptuation result is used in both expressions, it is preferable to keep use a single fitness function that comptutes both the objective and the constraints values. The memoized_fmincon() function in this repo is a wrapper to fmincon that allows the user to pass a single fitness function and optimize.

Example

The fitness function must have the following signature:

function [fval,gradf,c,ceq,gradc,gradceq] = fitness(x)
  fval = (1-x(1))^2 + 100*(x(2) - x(1)^2)^2;  % objective

  c(1,1) = (x(1) - 1)^3 - x(2) + 1;   % constraints
  c(2,1) = x(1) + x(2) - 2;

  ceq = [];

  gradf = [];
  gradc = [];
  gradceq = [];
end

Note that in this simple example, there are no shared terms within the computation of the obejctive and the constraints, so the memoization is not necessary. This simple example is rather intended to demonstrate the usage of the memoized_fmincon() function.

The main script should look as follows:

clear; close all; clc;

c = zeros(2,1);  % space for constraints
x0 = rand(2,1);

lb = [-1.5, -0.5];
ub = [1.5, 2.5];
opts = optimoptions('fmincon','Display','iter','Algorithm','sqp');

% run fmincon
[u,fval,exitflag,output] = memoized_fmincon(@fitness, x0, lb, ub, opts);

fprintf("Optimum x: %f, %f\n", u);

This example is from example_constrained.m.