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Optimal design of an electrical circuit.

Ratschek, H., Rokne, J., A circuit design problem. J. Global Opt., 3,
1993, pp.501.

Neculai Andrei, "Models, Test Problems and Applications for
Mathematical Programming". Technical Press, Bucharest, 2003.
Application A34, pp.397.
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Sets n /c1*c4/
     m /r1*r5/;

Table g(m,n)

       c1        c2        c3        c4
r1   0.4850    0.7520    0.8690    0.9820
r2   0.3690    1.2540    0.7030    1.4550
r3   5.2095   10.0677   22.9274   20.2153
r4  23.3037  101.7790  111.4610  191.2670
r5  28.5132  111.8467  134.3884  211.4823 ;

Variables x1,x2,x3,x4,x5,x6,x7,x8,x9,x10, obj;

Equations e1(n), e2(n), e3(n), e4(n), e, eobj;

e1(n)..  g('r4',n)*x2 - x10 +
             (1-x1*x2)*x3*(exp(x5*(g('r1',n) -
                                   g('r3',n)*x7/1000-
                                   g('r5',n)*x8/1000)) - 1) =l= g('r5',n);

e2(n).. -g('r4',n)*x2 - x10 -
             (1-x1*x2)*x3*(exp(x5*(g('r1',n) -
                                   g('r3',n)*x7/1000 -
                                   g('r5',n)*x8/1000)) - 1) =l= -g('r5',n);

e3(n).. -g('r5',n)*x1 - x10 +
             (1-x1*x2)*x4*(exp(x6*(g('r1',n) - g('r2',n) -
                                   g('r3',n)*x7/1000 +
                                   g('r4',n)*x9/1000)) - 1) =l= -g('r4',n);

e4(n)..  g('r5',n)*x1 - x10 -
             (1-x1*x2)*x4*(exp(x6*(g('r1',n) - g('r2',n) -
                                   g('r3',n)*x7/1000 +
                                   g('r4',n)*x9/1000)) - 1) =l= g('r4',n);

e..      x1*x3 - x2*x4 =e= 0;

eobj..   obj =e= x10;

* Bounds on variables
x1.lo=0;   x1.up=10;
x2.lo=0;   x2.up=10;
x3.lo=0;   x3.up=10;
x4.lo=0;   x4.up=10;
x5.lo=0;   x5.up=10;
x6.lo=0;   x6.up=10;
x7.lo=0;   x7.up=10;
x8.lo=0;   x8.up=10;
x9.lo=0;   x9.up=10;
x10.lo=0;  x10.up=10;

* Initial point
x1.l=0.7;
x2.l=0.38;
x3.l=0.8;
x4.l=1.5;
x5.l=6;
x6.l=6;
x7.l=4;
x8.l=1;
x9.l=1.6;
x10.l=1;

Model circuit /all/;

Solve circuit minimizing obj using nlp;
* End circuit