Models Constrained Goal Attainment Problems: goals prob and mco prob

This page is part of TOMLAB Models. See TOMLAB Models.

The TOMLAB bundle testprob provides two sets of problems for constrained goal attainment problems: goals_prob and mco_prob.

An example of a constrained goal attainment problems

The basic structure of a constrained goal attainment problems is the following:

Failed to parse (unknown function "\multicolumn"): {\displaystyle \begin{array}{cccccc} \min\limits_x & \multicolumn{5}{l}{\max \ \ lam: r(x) - w * lam \leq g} \\ \mbox{subject to} & x_L & \leq & x & \leq & x_U \\ {} & b_L & \leq & Ax & \leq & b_U \\ {} & c_L & \leq & c(x) & \leq & c_U \\\end{array} }

where $x,x_{L},x_{U}\in R^{n}$, $r(x)\in R^{N}$, $c(x),c_{L},c_{U}\in R^{m_{1}}$, $b_{L},b_{U}\in R^{m_{2}}$, $A\in R^{m_{2}\times n}$, $g\in R^{m}$, and $w\in R^{m}$.

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

File: tomlab/quickguide/goalsQG_r.m, goalsQG_J.m, goalsQG_c, goalsQG_dc

r:	Residual  vector
J:	Jacobian  matrix
c: 	Nonlinear constraint vector
dc: 	Nonlinear constraint  gradient matrix

The following file illustrates how to define and solve a problem of this category in TOMLAB.

File: tomlab/quickguide/goalsQG.m

mco_prob

In glb_prob there are 9 Multi-Criterium unconstrained and constrained nonlinear test problems with up to 10 variables and few constrains. In order to define the problem n and solve it execute the following in Matlab:

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

goals_prob

In goals_prob there are 9 constrained goal attainment test problems with sizes to 9 variables and about 10 constrains. In order to define the problem n and solve it execute the following in Matlab:

Prob = probInit('goals_prob',n); 
Result  = goalSolve(Prob,1);