Reference

Neculai Andrei, Nonlinear Optimization Applications Using the GAMS Technology,Springer Optimization and Its Applications, Model Benz (11.4) in chapter Robust Stability Analysis , 2013

Mainfile : benz.gms

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   Stability of a wire guided Daimler-Benz 0305 bus.

   References:
   Neculai Andrei, "Models, Test Problems and Applications for
   Mathematical Programming". Technical Press, Bucharest, 2003.

   Application A38, page 402.
   Ackermann, J., et al. " Robust gamma-stability analysis in a plant
   parameter space. Automatica, vol. 27, 1991, pp.75.

   Floudas, C.A., Pardalos, P.M., et al. "Handbook of Test Problems in
   Local and Global Optimization". Kluwer Academic Publishers, Dordrecht,
   1999.
   Section 7.3.5. Test problem 15, page 102.
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VARIABLES
         q1
         q2
         w   frequency
         k   stability margin
    objval   objective function variable;

FREE VARIABLES    objval;

EQUATIONS
         f Objective function
         g1
         g2
         b1l, b1u, b2l, b2u;

f  .. objval =e=k;

g1  .. (POWER(q1,2)*POWER(q2,2))*POWER(w,8) -
       (1.25*1000*POWER(q1,2)*POWER(q2,2) + 16.8*POWER(q1,2)*q2 +
        53.9*1000*q1*q2 + 270*1000)*POWER(w,6) +
       (1.45*POWER(10,6)*POWER(q1,2)*q2 + 16.8*POWER(10,6)*q1*q2 +
        POWER(10,6)*338)*POWER(w,4) -
       (5.72*POWER(10,6)*POWER(q1,2)*q2 + 113*POWER(10,6)*POWER(q1,2) +
        4250*POWER(10,6)*q1)*POWER(w,2) +
       (453*POWER(10,6)*POWER(q1,2)) =e= 0;

g2  .. (50*POWER(q1,2)*POWER(q2,2) + 1080*q1*q2)*POWER(w,6) -
       (15.6*1000*POWER(q1,2)*POWER(q2,2) + 840*POWER(q1,2)*q2 +
        1.35*POWER(10,6)*q1*q2 + POWER(10,6)*13.5)*POWER(w,4) +
       (6.93*POWER(10,6)*POWER(q1,2)*q2 + 911*POWER(10,6)*q1 +
        POWER(10,6)*4220)*POWER(w,2) -
       (528*POWER(10,6)*POWER(q1,2) + 3640*POWER(10,6)*q1) =e= 0;

b1l  .. 17.5 - 14.5*k =l= q1;
b1u  .. q1 =l= 17.5 + 14.5*k;
b2l  .. 20.0 - 15.0*k =l= q2;
b2u  .. q2 =l= 20.0 + 15.0*k;

* Bounds
q1.LO=0;
q1.UP=2;
q2.LO=0;
q2.UP=2;
w.LO =0;
w.UP =2;
k.LO =0;
k.UP =2;

* Initial values;
q1.l=0.1;
q2.l=0.1;
w.l=0.1;
k.l=0.1;

MODEL benz /ALL/;

$ifThenI x%mode%==xbook
benz.workspace=120;
$endIf

SOLVE benz USING NLP MINIMIZING objval;
* End Benz