ex7_3_6.gms:
References:
- Floudas, C A, Pardalos, P M, Adjiman, C S, Esposito, W R, Gumus, Z H, Harding, S T, Klepeis, J L, Meyer, C A, and Schweiger, C A, Handbook of Test Problems in Local and Global Optimization. Kluwer Academic Publishers, 1999.
- Barmish, B R, New Tools for Robustness of Linear Systems. MacMillan Publishing Company, New York, NY, 1994.
- Abate, M, Barmish, B R, Murillo-Sanchez, C, and Tempo, R, Application of Some New Tools to Robust Stability Analysis of Spark Ignition Engines : A Case Study. IEEE Trans. Contr. Syst. Tech. 2 (1994), 22.
- Original source: Global Model of Chapter 7 ex7.3.6.gms from Floudas e.a. Test Problems
Point:
p1
Best known point: p1 with value 0.0000
<![CDATA[
* NLP written by GAMS Convert at 07/19/01 13:39:52
*
* Equation counts
* Total E G L N X
* 18 11 0 7 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 18 18 0 0 0 0 0 0
* FX 0 0 0 0 0 0 0 0
*
* Nonzero counts
* Total const NL DLL
* 80 26 54 0
*
* Solve m using NLP minimizing objvar;
Variables x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17,objvar;
Negative Variables x1,x2,x3,x5;
Positive Variables x8,x9;
Equations e1,e2,e3,e4,e5,e6,e7,e8,e9,e10,e11,e12,e13,e14,e15,e16,e17,e18;
e1.. - x9 + objvar =E= 0;
e2.. x14*POWER(x8,4) - x16*POWER(x8,6) - x12*sqr(x8) + x10 =E= 0;
e3.. x17*POWER(x8,6) - x15*POWER(x8,4) + x13*sqr(x8) - x11 =E= 0;
e4.. - x1 - 1.2721*x9 =L= -3.4329;
e5.. - x2 - 0.06*x9 =L= -0.1627;
e6.. - x3 - 0.0782*x9 =L= -0.1139;
e7.. x4 - 0.3068*x9 =L= 0.2539;
e8.. - x5 - 0.0108*x9 =L= -0.0208;
e9.. x6 - 2.4715*x9 =L= 2.0247;
e10.. x7 + 9*x9 =L= 1;
e11.. - (6.82079e-5*x1*x3*sqr(x4) + 6.82079e-5*x1*x2*x4*x5) + x10 =E= 0;
e12.. - (0.00076176*sqr(x2)*sqr(x5) + 0.00076176*sqr(x3)*sqr(x4) + 0.000402141
*x1*x2*sqr(x5) + 0.00337606*x1*x3*sqr(x4) + 6.82079e-5*x1*x4*x5 +
0.00051612*sqr(x2)*x5*x6 + 0.00337606*x1*x2*x4*x5 + 6.82079e-5*x1*x2*x4*
x7 + 6.28987e-5*x1*x2*x5*x6 + 0.000402141*x1*x3*x4*x5 + 6.28987e-5*x1*x3*
x4*x6 + 0.00152352*x2*x3*x4*x5 + 0.00051612*x2*x3*x4*x6) + x11 =E= 0;
e13.. - (0.000402141*x1*sqr(x5) + 0.00152352*x2*sqr(x5) + 0.0552*sqr(x2)*sqr(
x5) + 0.0552*sqr(x3)*sqr(x4) + 0.0189477*x1*x2*sqr(x5) + 0.034862*x1*x3*
sqr(x4) + 0.00336706*x1*x4*x5 + 6.82079e-5*x1*x4*x7 + 6.28987e-5*x1*x5*x6
+ 0.00152352*x3*x4*x5 + 0.00051612*x3*x4*x6 - 0.00234048*sqr(x3)*x4*x6
+ 0.034862*x1*x2*x4*x5 + 0.0237398*sqr(x2)*x5*x6 + 0.00152352*sqr(x2)*x5
*x7 + 0.00051612*sqr(x2)*x6*x7 + 0.00336706*x1*x2*x4*x7 + 0.00287416*x1*
x2*x5*x6 + 0.000804282*x1*x2*x5*x7 + 6.28987e-5*x1*x2*x6*x7 + 0.0189477*
x1*x3*x4*x5 + 0.00287416*x1*x3*x4*x6 + 0.000402141*x1*x3*x4*x7 + 0.1104*
x2*x3*x4*x5 + 0.0237398*x2*x3*x4*x6 + 0.00152352*x2*x3*x4*x7 - 0.00234048
*x2*x3*x5*x6 + 0.00103224*x2*x5*x6) + x12 =E= 0;
e14.. - (0.189477*x1*sqr(x5) + 0.1104*x2*sqr(x5) + 0.00051612*x5*x6 + sqr(x2)*
sqr(x5) + 0.00076176*sqr(x2)*sqr(x7) + sqr(x3)*sqr(x4) + 0.1586*x1*x2*
sqr(x5) + 0.000402141*x1*x2*sqr(x7) + 0.0872*x1*x3*sqr(x4) + 0.034862*x1*
x4*x5 + 0.00336706*x1*x4*x7 + 0.00287416*x1*x5*x6 + 6.28987e-5*x1*x6*x7
+ 0.00103224*x2*x6*x7 + 0.1104*x3*x4*x5 + 0.0237398*x3*x4*x6 +
0.00152352*x3*x4*x7 - 0.00234048*x3*x5*x6 + 0.1826*sqr(x2)*x5*x6 + 0.1104
*sqr(x2)*x5*x7 + 0.0237398*sqr(x2)*x6*x7 - 0.0848*sqr(x3)*x4*x6 + 0.0872*
x1*x2*x4*x5 + 0.034862*x1*x2*x4*x7 + 0.0215658*x1*x2*x5*x6 + 0.0378954*x1
*x2*x5*x7 + 0.00287416*x1*x2*x6*x7 + 0.1586*x1*x3*x4*x5 + 0.0215658*x1*x3
*x4*x6 + 0.0189477*x1*x3*x4*x7 + 2*x2*x3*x4*x5 + 0.1826*x2*x3*x4*x6 +
0.1104*x2*x3*x4*x7 - 0.0848*x2*x3*x5*x6 - 0.00234048*x2*x3*x6*x7 +
0.00076176*sqr(x5) + 0.0474795*x2*x5*x6 + 0.000804282*x1*x5*x7 +
0.00304704*x2*x5*x7) + x13 =E= 0;
e15.. - (0.1586*x1*sqr(x5) + 0.000402141*x1*sqr(x7) + 2*x2*sqr(x5) +
0.00152352*x2*sqr(x7) + 0.0237398*x5*x6 + 0.00152352*x5*x7 + 0.00051612*
x6*x7 + 0.0552*sqr(x2)*sqr(x7) + 0.0189477*x1*x2*sqr(x7) + 0.0872*x1*x4*
x5 + 0.034862*x1*x4*x7 + 0.0215658*x1*x5*x6 + 0.00287416*x1*x6*x7 +
0.0474795*x2*x6*x7 + 2*x3*x4*x5 + 0.1826*x3*x4*x6 + 0.1104*x3*x4*x7 -
0.0848*x3*x5*x6 - 0.00234048*x3*x6*x7 + 2*sqr(x2)*x5*x7 + 0.1826*sqr(x2)*
x6*x7 + 0.0872*x1*x2*x4*x7 + 0.3172*x1*x2*x5*x7 + 0.0215658*x1*x2*x6*x7
+ 0.1586*x1*x3*x4*x7 + 2*x2*x3*x4*x7 - 0.0848*x2*x3*x6*x7 + 0.0552*sqr(
x5) + 0.3652*x2*x5*x6 + 0.0378954*x1*x5*x7 + 0.2208*x2*x5*x7) + x14
=E= 0;
e16.. - (0.0189477*x1*sqr(x7) + 0.1104*x2*sqr(x7) + 0.1826*x5*x6 + 0.1104*x5*
x7 + 0.0237398*x6*x7 + sqr(x2)*sqr(x7) + 0.1586*x1*x2*sqr(x7) + 0.0872*x1
*x4*x7 + 0.0215658*x1*x6*x7 + 0.3652*x2*x6*x7 + 2*x3*x4*x7 - 0.0848*x3*x6
*x7 + sqr(x5) + 0.00076176*sqr(x7) + 0.3172*x1*x5*x7 + 4*x2*x5*x7) + x15
=E= 0;
e17.. - (0.1586*x1*sqr(x7) + 2*x2*sqr(x7) + 2*x5*x7 + 0.1826*x6*x7 + 0.0552*
sqr(x7)) + x16 =E= 0;
e18.. - sqr(x7) + x17 =E= 0;
* set non default bounds
x1.up = 3.4329;
x2.up = 0.1627;
x3.up = 0.1139;
x4.lo = 0.2539;
x5.up = 0.0208;
x6.lo = 2.0247;
x7.lo = 1;
x8.up = 10;
x9.up = 1;
* set non default levels
* set non default marginals
Model m / all /;
m.limrow=0; m.limcol=0;
$if NOT '%gams.u1%' == '' $include '%gams.u1%'
Solve m using NLP minimizing objvar;
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