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17 Geometric programming
In
gp_prob there are 14 geometric programming
test problems with sizes to 12 variables and about 10 constrains.
In order to define the problem
n and solve it execute the following in Matlab:
Prob = probInit('gp_prob',n);
Result = tomRun('',Prob);
The primal geometric programming problem is defined below (the dual is used internally).
|
|
|
|
| (GP) |
VGP:= |
minimize |
g0(t) |
|
| |
|
subject to |
gk(t) ≤ 1, |
k = 1,2,…, p |
| |
|
|
ti > 0, |
i = 1,2,…, m |
|
|
|
|
(19) |
|
where
|
|
| g0(t) |
= |
|
(20) |
| gk(t) |
= |
| |
|
cj t1a1j ...
tmamj, k = 1,2,…, p.
|
|
(21) |
|
Given exponents
aij for the
ith variable in the
jth product
term,
i=1,…,
m and
j=1,…,
np, are arbitrary real
constants and term coefficients
cj are positive.
Example problem:
| (P1) |
min |
5x1 + 50000x1−1 + 20x2 + 72000x2−1 + 10x3 + 144000x3−1 |
| |
| |
subject to |
4x1−1 + 32x2−1 + 120x3−1 <= 1 |
| |
| |
|
x ≥ 0 |
|
The following file illustrates how to define and solve a problem
of this category in TOMLAB.
File: tomlab/quickguide/gpQG.m
% 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);
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