ex_box_denseformat.m

HERE IS A GOOD PSO TOOL BOX

%----------------------------------------------------------------------
%
%       BOX VOLUME MAXIMIZATION EXAMPLE IN DENSE FORMAT
%
%----------------------------------------------------------------------
%
%   maximize:   h^-1*w^-1*d^-1
%   subject to: (2/Awall)*h*w+(2/Awall)*h*d <= 1,
%               (1/Aflr)*w*d <= 1,
%               alpha*h^-1*w <= 1,
%               (1/beta)*h*w^-1 <= 1,
%               gamma*w*d^-1 <= 1,
%               (1/delta)*w^-1*d <= 1.
%
%   This is an example taken directly from the paper:
%       A Tutorial on Geometric Programming (see pages 8 and 13)
%       by Boyd, Kim, Vandenberghe, and Hassibi.
%

clear all; close all;

%----------------------------------------------------------------------
%      PROBLEM DATA IN POSYNOMIAL FORM (DENSE FORMAT)
%----------------------------------------------------------------------
Aflr  = 1000;
Awall = 100;
alpha = 0.5;
beta  = 2;
gamma = 0.5;
delta = 2;

% form a matrix A
A   = [-1  -1  -1;...
        1   1   0;...
        1   0   1;...
        0   1   1;...
       -1   1   0;...
        1  -1   0;...
        0   1  -1;...
        0  -1   1];

b   = [1 2/Awall 2/Awall 1/Aflr alpha 1/beta gamma 1/delta]';
szs = [1 2 1 1 1 1 1]'; 

%----------------------------------------------------------------------
%      SOLVE THE PROBLEM IN POSYNOMIAL FORM
%----------------------------------------------------------------------
[x1,status1,lambda1,nu1] = gpposy(A,b,szs);
% calculate the volume
vol_posy = prod(x1)

%----------------------------------------------------------------------
%      SOLVE THE PROBLEM IN CONVEX FORM
%----------------------------------------------------------------------
[x2,status2,lambda2,nu2,mu2] = gpcvx(A,log(b),szs);
% convert the result from convex form into posynomial form
vol_cvx = prod(exp(x2))