$title MathOptimizer Example 1 (MATHOPT1,SEQ=255)

$onText
A simple example model that illustrates the formulation structure for
using LGO in the Mathematica environment.

More information at https://www.wolfram.com/products/applications/mathoptimizer/

Mathematica, MathOptimizer - An Advanced Modeling and Optimization System
for Mathematica Users, https://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
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$eolCom //

Variable x1, x2, obj;

x1.lo = -10; x2.lo = -15;    // lower bounds
x1.l  =   8; x2.l  = -14;    // initial value
x1.up =  20; x2.up =  20;    // upper bounds

Equation objdef, eqs, ineqs;

objdef.. obj =e= 10*sqr(sqr(x1) - x2) + sqr(x1 - 1);

eqs..    x1  =e= x1*x2;

ineqs..  3*x1 + 4*x2 =l= 25;

Models m / all /;

* x1.l = 1; x2.l = 1;    // optimal values

solve m minimizing obj using nlp;

Parameter report 'solution summary report';
report('x1','global') = 1;
report('x2','global') = 1;
report('x1','solver') = x1.l;
report('x2','solver') = x2.l;
report('x1','diff')   = report('x1','global') - report('x1','solver');
report('x2','diff')   = report('x2','global') - report('x2','solver');

display report;