Quickguide GLB Problem

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

The unconstrained global optimization (glb) problem is defined as

${\begin{array}{ll}\min \limits _{x}&f(x)\\&\\s/t&{\begin{array}{llcccll}-\infty <&x_{L}&\leq &x&\leq &x_{U}&<\infty \\\end{array}}\end{array}}$

where Failed to parse (unknown function "\MATHSET"): {\displaystyle x, x_L, x_U \in \MATHSET{R}^n} , Failed to parse (unknown function "\MATHSET"): {\displaystyle f(x) \in \MATHSET{R}} .

The following files define a problem in TOMLAB.

File: tomlab/quickguide/glbQG_f.m

f:   Function

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

File: tomlab/quickguide/glbQG.m

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

 % glbQG is a small example problem for defining and solving
 % unconstrained global programming problems using the TOMLAB format.
 
 Name  = 'Shekel 5';
 x_L   = [ 0  0  0  0]';  % Lower bounds for x.
 x_U   = [10 10 10 10]';  % Upper bounds for x.
 x_0   = [-3.0144 -2.4794 -3.1584 -3.1790]; % Most often not used.
 x_opt = [];
 f_opt = -10.1531996790582;
 f_Low = -20;             % Lower bound on function.
 x_min = [ 0  0  0  0]; % For plotting
 x_max = [10 10 10 10]; % For plotting
 
 Prob  = glcAssign('glbQG_f', x_L, x_U, Name, [], [], [], ... 
                    [], [], [], x_0, ...
                    [], [], [], [], ...
                    f_Low, x_min, x_max, f_opt, x_opt);
 
 Prob.optParam.MaxFunc = 1500;              
               
 Result1 = tomRun('glbFast', Prob, 1);  % Global solver            
 Result2 = tomRun('conSolve', Prob, 2); % Local solver, starting from Prob.x_0
 % Also possible to use a mixed-integer global solver
 Result = tomRun('glcDirect', Prob, 1); 
 
 % Result = tomRun('glbDirect', Prob, 1);
 % Result = tomRun('glcDirect', Prob, 1);
 % Result = tomRun('glbSolve', Prob, 1);
 % Result = tomRun('glcSolve', Prob, 1);
 % Result = tomRun('glcFast', Prob, 1);
 % Result = tomRun('lgo', Prob, 1);
 % Result = tomRun('oqnlp', Prob, 1);