Quickguide GLC Problem

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

The global mixed-integer nonlinear programming (glc) problem is defined as

${\begin{array}{ll}\min \limits _{x}&f(x)\\&\\s/t&{\begin{array}{llcccll}-\infty <&x_{L}&\leq &x&\leq &x_{U}&<\infty \\&b_{L}&\leq &Ax&\leq &b_{U}&\\&c_{L}&\leq &c(x)&\leq &c_{U},&~x_{j}\in \mathbb {N} \ ~~\forall j\in \$I\$,\\\end{array}}\end{array}}$

where $x,x_{L},x_{U}\in \mathbb {R} ^{n}$, $f(x)\in \mathbb {R}$, $A\in \mathbb {R} ^{m_{1}\times n}$, $b_{L},b_{U}\in \mathbb {R} ^{m_{1}}$ and $c_{L},c(x),c_{U}\in \mathbb {R} ^{m_{2}}$. The variables $x\in I$, the index subset of $1,...,n$, are restricted to be integers.

The following files define a problem in TOMLAB.

File: tomlab/quickguide/glcQG_f.m, glcQG_c.m

f:   Function
c:   Constraints

The following file illustrates how to solve a constrained global optimization problem in TOMLAB. Also view the m-files specified above for more information.

File: tomlab/quickguide/glcQG.m

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

 % glcQG is a small example problem for defining and solving
 % constrained global programming problems using the TOMLAB format.
 
 Name = 'Hock-Schittkowski 59';
 u = [75.196    3.8112    0.0020567  1.0345E-5  6.8306    0.030234   1.28134E-3 ...
      2.266E-7  0.25645   0.0034604  1.3514E-5  28.106    5.2375E-6  6.3E-8     ...
      7E-10     3.405E-4  1.6638E-6  2.8673     3.5256E-5];
 
 x_L = [0 0]';     % Lower bounds for x.
 x_U = [75 65]';   % Upper bounds for x.
 b_L = []; b_U = []; A = []; % Linear constraints
 c_L = [0 0 0];    % Lower bounds for nonlinear constraints.
 c_U = [];         % Upper bounds for nonlinear constraints.
 x_opt = [13.55010424 51.66018129]; % Optimum vector
 f_opt = -7.804226324;              % Optimum
 x_min = x_L;      % For plotting
 x_max = x_U;      % For plotting
 x_0 = [90 10]';   % If running local solver
 
 Prob = glcAssign('glcQG_f', x_L, x_U, Name, A, b_L, b_U, ... 
                   'glcQG_c', c_L, c_U, x_0, ...
                   [], [], [], [], ...
                   [], x_min, x_max, f_opt, x_opt);
 
 Prob.user.u = u;
 Prob.optParam.MaxFunc = 1500;
 
 Result = tomRun('glcFast', Prob, 1);
 %Result = tomRun('glcSolve', Prob, 1);
 %Result = tomRun('lgo', Prob, 1);
 %Result = tomRun('oqnlp', Prob, 1);