# Models Constrained Global Optimization Problems: glc prob

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In glc_prob there are 30 global mixed-integer nonlinear programming test problems with sizes to 20 variables and 5 constrains. In order to define the problem n and solve it execute the following in Matlab:

Prob = probInit('glc_prob',n); Result = tomRun('',Prob);

The basic structure of a constrained global optimization problems is the following

where , , ,
and . The variables ,
the index subset of 1,...,*n*, are restricted to be integers.

The following files are required to define a problem of this category in TOMLAB.

**File: **tomlab/quickguide/glcQG f.m, glcQG c.m

f: Function c: Constraints

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

**File: **tomlab/quickguide/glcQG.m

% 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);