$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 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;
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;