View source for Models Global Optimization Problems: glb prob, lgo1 prob, lgo2 prob and gkls prob

==Example of a global optimization  problem==

The basic structure of a global optimization problem with simple bounds is the following


<math>
\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}
</math>

where <math>x, x_L, x_U \in \mathbb{R}^n</math>, <math>f(x) \in \mathbb{R}</math>. The
variables <math>x \in I</math>, the index subset of <math>1,...,n</math>, are restricted
to be integers.

The following file is required to define a problem of this category in TOMLAB.

'''File: '''tomlab/quickguide/glbQGf.m

<pre>
f:	Function
</pre>

An example of a problem of this class, (that is also found in the TOMLAB quickguide) is glbQG:

'''File: '''tomlab/quickguide/glbQG.m

<source lang="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]; % May not be 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, 1); %Local solver

% 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);
</source>

==glb_prob==

In <tt>glb_prob</tt> there are 51 unconstrained global optimization test problems with sizes to 100 variables. In order to define the problem n and solve it execute the following in Matlab:

<pre>
Prob	= probInit('glb_prob',n); 
Result  = tomRun('',Prob);
</pre>

==lgo1_prob==

In <tt>glo1_prob</tt> there are 30 global optimization test problems in one dimension.  In order to define the problem n and solve it execute the following in Matlab:

<pre>
Prob	= probInit('lgo1_prob',n); 
Result  = tomRun('',Prob);
</pre>

==lgo2_prob==

In <tt>glo2_prob</tt> there are 30 global optimization test problems in two up to four dimensions. In order to define the problem n and solve it execute the following in Matlab:

<pre>
Prob	= probInit('lgo2_prob',n); 
Result  = tomRun('',Prob);
</pre>

==gkls_prob==

In <tt>gkls_prob</tt> there are 300 global optimization test problems in two dimensions.  In order to define the problem n and solve it execute the following in Matlab:

<pre>
Prob	= probInit('gkls_prob',n); 
Result  = tomRun('',Prob);
</pre>