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mathopt4.gms : MathOptimizer Example 4

This the 4th example from Mathematica and LGO. The global solution is at x=0.

More information at http://www.wolfram.com/products/applications/mathoptimizer/
References:
Small Model of Type: NLP
$title MathOptimizer Example 4 (MATHOPT4,SEQ=258) * This the 4th example from Mathematica and LGO. The global solution is at 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 * $eolcom // variables x1, x2, obj; equations objdef, eq1, ineq1; objdef.. obj =e= sqr(2*sqr(x1)-sqr(x2)) + sqr(x2 - 6*sqr(x1)); eq1.. x1 =e= 10*x2 + 100*Sin[2*x1+3*x2]; ineq1.. x2 + x1 =l= 2; model m /all/; x1.lo=-10; x2.lo=-10; x1.up=+10; x2.up=+10; set row / one,two,three, global /; parameter report(row,*) summary solution report; x1.l = -4; x2.l = -2; // leads to local solution report('one','x1_0') = x1.l; report('one','x2_0') = x2.l; solve m us nlp min obj; report('one','x1.l') = x1.l; report('one','x2.l') = x2.l; report('one','modelstat') = m.modelstat; x1.l = -2; x2.l = -1; // leads to local optimum report('two','x1_0') = x1.l; report('two','x2_0') = x2.l; solve m us nlp min obj; report('two','x1.l') = x1.l; report('two','x2.l') = x2.l; report('two','modelstat') = m.modelstat; x1.l = 1; x2.l = -1; // leads to global optimum report('three','x1_0') = x1.l; report('three','x2_0') = x2.l; solve m us nlp min obj; report('three','x1.l') = x1.l; report('three','x2.l') = x2.l; report('three','modelstat') = m.modelstat; x1.l = 0; x2.l = 0; // is the global optimum report('global','x1_0') = x1.l; report('global','x2_0') = x2.l; solve m us nlp min obj; report('global','x1.l') = x1.l; report('global','x2.l') = x2.l; report('global','modelstat') = m.modelstat; acronym global; report(row,'status')$((abs(report('global','x1_0')-report(row,'x1.l')) +abs(report('global','x2_0')-report(row,'x2.l'))) < 1e-6) = global; display report;