Quickguide GLB Problem

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

The unconstrained global optimization (glb) problem is defined as

Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \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 (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x, x_L, x_U \in \mathbb{R}^n} , Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f(x) \in \mathbb{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);