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mathopt2.gms : MathOptimizer Example 2

The following is still a fairly simple constrained model which has
two variables, two equality and two inequality constraints.
The optimum value is zero at the vector x = 0.

More information at http://www.wolfram.com/products/applications/mathoptimizer/
References:
Small Model of Type: NLP
$title MathOptimizer Example 2 (MATHOPT2,SEQ=256) * The following is still a fairly simple constrained model which has * two variables, two equality and two inequality constraints. * The optimum value is zero at the vector x = 0. * * More information at http://www.wolfram.com/products/applications/mathoptimizer/ * * * Mathematica, MathOptimizer - An Advanced Modeling and Optimization System * for Mathematica Users, http://www.wolfram.com/products/applications/mathoptimizer/ * * Janos D Pinter, Global Optimization in Action, Kluwer Academic Publishers, * Dordrecht/Boston/London, 1996. * * Janos D Pinter, Computational Global Optimization in Nonlinear Systems, * Lionheart Publishing, Inc., Atlanta, GA, 2001 $eolcom // variables x1, x2, obj; x1.l = 10; x2.l = -10; // initial value *x1.lo =-100; x2.lo =-100; // lower bounds *x1.up = 100; x2.up = 100; // upper bounds equations objdef, eq1, eq2, ineq1, ineq2; objdef.. obj =e= sqr(2*sqr(x1) - x2) + sqr(x2 - 6*sqr(x1)); eq1.. x1 =e= 10*x2 + x1*x2 ; eq2.. x1 =e= 3*x2 ; ineq1.. x2 + x1 =l= 1; ineq2.. x2 - x1 =l= 2; models m / all /; solve m minimizing obj using nlp; parameter report diff from global solution; report('x1') = round(0 - x1.l,6); report('x2') = round(0 - x2.l,6); Display report;