Quickguide GP Problem

This page is part of the Quickguide Manual. See Quickguide.

Geometric programming problems are a set of special problems normally solved with TOMLAB /GP. The optimum is commonly non-differentiable. Problems are modeled on the primal form, but the dual is entered and solved.

The primal geometric programming problem is defined as:

${\begin{array}{lllll}(GP)&V_{GP}:=&{\mbox{minimize}}~&g_{0}(t)&\\&&{\mbox{subject to}}&g_{k}(t)\leq 1,&k=1,2,\ldots ,p\\&&&t_{i}>0,&i=1,2,\ldots ,m\end{array}}$

where

$g_{0}(t)=\sum _{j=1}^{n_{0}}c_{j}t_{1}^{a_{1j}}...t_{m}^{a_{mj}}$

$g_{k}(t)=\sum _{j=n_{k-1}+1}^{n_{k}}c_{j}t_{1}^{a_{1j}}...t_{m}^{a_{mj}},\quad k=1,2,\ldots ,p.$

Given exponents $a_{ij}$ for the $i$th variable in the $j$th product term, $i=1,\ldots ,m$ and $j=1,\ldots ,n_{p}$, are arbitrary real constants and term coefficients $c_{j}$ are positive.

Example problem:

The following file defines and solves the problem in TOMLAB.

File: tomlab/quickguide/gpQG.m

Open the file for viewing, and execute gpQG in Matlab.

 % gpQG is a small example problem for defining and solving
 % geometric programming problems using the TOMLAB format.
 
 nterm = [6;3];
 coef = [.5e1;.5e5;.2e2;.72e5;.1e2;.144e6;.4e1;.32e2;.12e3];
 A = sparse([ 1  -1  0   0  0  0 -1  0  0;...      
              0   0  1  -1  0  0  0 -1  0;...
              0   0  0   0  1 -1  0  0 -1])';
                   
 Name  = 'GP Example';  % File gpQG.m
 
 % Assign routine for defining a GP problem.
 Prob = gpAssign(nterm, coef, A, Name);
 
 % Calling driver routine tomRun to run the solver.
 % The 1 sets the print level after optimization.
 
 Result = tomRun('GP', Prob, 1);