$title MathOptimizer Example 2 (MATHOPT2,SEQ=256)

$onText
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 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.l = 10; x2.l = -10;           // initial value
* x1.lo = -100; x2.lo = -100;    // lower bounds
* x1.up =  100; x2.up =  100;    // upper bounds

Equation 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;

Model 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;