Description

The Hundred-dollar, Hundred-digit Challenge Problems as stated by
N. Trefethen, Oxford University.

Several random points are used to test the robustness of global and
local codes. You may want to run gams with lo = 0 or lo = 2 to reduce
output to the log.

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

Small Model of Type : DNLP

Category : GAMS Model library

Main file : mathopt6.gms

$title MathOptimizer Example 6 (MATHOPT6,SEQ=260)

$onText
The Hundred-dollar, Hundred-digit Challenge Problems as stated by
N. Trefethen, Oxford University.

Several random points are used to test the robustness of global and
local codes. You may want to run gams with lo = 0 or lo = 2 to reduce
output to the log.

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


N. Trefethen, SIAM News, January - February 2002, page 3.

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, discontinuous derivatives, mathematics, global
          optimization
$offText

$eolCom //

Variable x, y, obj;

Equation objdef;

objdef.. obj =e= exp(sin(50*x)) + sin(60*exp(y))  + sin(70*sin(x))
              +  sin(sin(80*y)) - sin(10*(x + y)) + (sqr(x) + sqr(y))/4;

x.lo = -3;
x.up =  3;
y.lo = -3;
y.up =  3;

Model m / objdef /;

Parameter report 'summary report';
report('best','x0')  = -0.0244030796935730;
report('best','y0')  =  0.2106124271552849;
report('best','obj') = -3.306868647475235;
report('best','x.l') = report('best','x0');
report('best','y.l') = report('best','y0');

Scalar global 'best known solution';
global = report('best','obj')

Set i 'random samples' / rand1*rand100 /;

* You may want to run gams with lo = 0 or lo = 2 to reduce output to the log
m.limRow   = 0;
m.limCol   = 0;
m.solPrint = %solPrint.Report%;

Scalar best / inf /;

* try random starting points and report better solution only
loop(i$(best > (global + 1e-6)),
   x.l = uniform(x.lo,x.up);  // get
   y.l = uniform(y.lo,y.up);  // random
   report(i,'x0') = x.l;      // starting point
   report(i,'y0') = y.l;      // and save

   solve m using dnlp min obj;
   m.solPrint = %solPrint.quiet%; // turn off solution listing

   if(m.solveStat <> %solveStat.normalCompletion%,
      display 'solver failed - no further solutions';
      best = -inf;
   );   // stop the loop
   if(obj.l >= best or not(m.modelStat=%modelStat.optimal% or
                           m.modelStat=%modelStat.feasibleSolution% or
                           m.modelStat=%modelStat.locallyOptimal%),
      report(i,'x0') = 0;  // remove entries from report
      report(i,'y0') = 0;  // remove entries from report
   else
      best := obj.l;
      report(i,'obj')   = obj.l;
      report(i,'x.l')   = x.l;
      report(i,'y.l')   = y.l;
      report(i,'optcr') = -(obj.l - report('best','obj'))/report('best','obj');
      report(i,'cpu')   = m.resUsd;
   );
);

display report;