$title MathOptimizer Example 4 (MATHOPT4,SEQ=258) $onText 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 Keywords: nonlinear programming, mathematics, global optimization $offText $eolCom // Variable x1, x2, obj; Equation objdef, eq1, ineq1; objdef.. obj =e= sqr(2*sqr(x1) - sqr(x2)) + sqr(x2 - 6*sqr(x1)); eq1.. x1 =e= 10*x2 + 100*sin(2*x1 + 3*x2); ineq1.. x2 + x1 =l= 2; Model m / all /; x1.lo = -10; x2.lo = -10; x1.up = 10; x2.up = 10; Set row / one, two, three, global /; Parameter report(row,*) 'summary solution report'; x1.l = -4; x2.l = -2; // leads to local solution report('one','x1_0') = x1.l; report('one','x2_0') = x2.l; solve m using nlp min obj; report('one','x1.l') = x1.l; report('one','x2.l') = x2.l; report('one','modelstat') = m.modelStat; x1.l = -2; x2.l = -1; // leads to local optimum report('two','x1_0') = x1.l; report('two','x2_0') = x2.l; solve m using nlp min obj; report('two','x1.l') = x1.l; report('two','x2.l') = x2.l; report('two','modelstat') = m.modelStat; x1.l = 1; x2.l = -1; // leads to global optimum report('three','x1_0') = x1.l; report('three','x2_0') = x2.l; solve m using nlp min obj; report('three','x1.l') = x1.l; report('three','x2.l') = x2.l; report('three','modelstat') = m.modelStat; x1.l = 0; x2.l = 0; // is the global optimum report('global','x1_0') = x1.l; report('global','x2_0') = x2.l; solve m using nlp min obj; report('global','x1.l') = x1.l; report('global','x2.l') = x2.l; report('global','modelstat') = m.modelStat; Acronym global; report(row,'status')$((abs(report('global','x1_0') - report(row,'x1.l')) +abs(report('global','x2_0') - report(row,'x2.l'))) < 1e-6) = global; display report;