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Instance ex7_2_1

Formatsⓘ	ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)ⓘ	1227.22607500 p1 ( gdx sol ) (infeas: 2e-10)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	1227.22222100 (ANTIGONE) 1227.22566900 (BARON) 1225.42758000 (COUENNE) 1227.22585300 (LINDO) 1227.22607500 (SCIP)
Referencesⓘ	Floudas, C A, Pardalos, Panos M, Adjiman, C S, Esposito, W R, Gumus, Zeynep H, Harding, S T, Klepeis, John L, Meyer, Clifford A, and Schweiger, C A, Handbook of Test Problems in Local and Global Optimization, Kluwer Academic Publishers, 1999. Dembo, R S, A Set of Geometric Programming Test Problems and Their Solutions, Mathematical Programming, 10:1, 1976, 192-213.
Sourceⓘ	Test Problem ex7.2.1 of Chapter 7 of Floudas e.a. handbook
Added to libraryⓘ	31 Jul 2001
Problem typeⓘ	NLP
#Variablesⓘ	7
#Binary Variablesⓘ	0
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	7
#Nonlinear Binary Variablesⓘ	0
#Nonlinear Integer Variablesⓘ	0
Objective Senseⓘ	min
Objective typeⓘ	quadratic
Objective curvatureⓘ	indefinite
#Nonzeros in Objectiveⓘ	5
#Nonlinear Nonzeros in Objectiveⓘ	4
#Constraintsⓘ	14
#Linear Constraintsⓘ	2
#Quadratic Constraintsⓘ	2
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	10
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ
Constraints curvatureⓘ	indefinite
#Nonzeros in Jacobianⓘ	40
#Nonlinear Nonzeros in Jacobianⓘ	31
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	33
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	7
#Blocks in Hessian of Lagrangianⓘ	1
Minimal blocksize in Hessian of Lagrangianⓘ	7
Maximal blocksize in Hessian of Lagrangianⓘ	7
Average blocksize in Hessian of Lagrangianⓘ	7.0
#Semicontinuitiesⓘ	0
#Nonlinear Semicontinuitiesⓘ	0
#SOS type 1ⓘ	0
#SOS type 2ⓘ	0
Minimal coefficientⓘ	1.2245e-05
Maximal coefficientⓘ	4.8951e+05
Infeasibility of initial pointⓘ	2.99
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*         15        1        0       14        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*          8        8        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         46       11       35        0
*
*  Solve m using NLP minimizing objvar;


Variables  x1,x2,x3,x4,x5,x6,x7,objvar;

Equations  e1,e2,e3,e4,e5,e6,e7,e8,e9,e10,e11,e12,e13,e14,e15;


e1.. -(0.035*x1*x6 - 0.063*x3*x5 + 1.715*x1 + 4.0565*x3) - 10*x2 + objvar
      =E= 3000;

e2.. 0.0059553571*sqr(x6) + 0.88392857*x3/x1 - 0.1175625*x6 =L= 1;

e3.. 1.1088*x1/x3 + 0.1303533*x1/x3*x6 - 0.0066033*x1/x3*sqr(x6) =L= 1;

e4.. 0.00066173269*sqr(x6) - 0.019120592*x6 - 0.0056595559*x4 + 0.017239878*x5
      =L= 1;

e5.. 56.85075/x5 + 1.08702*x6/x5 + 0.32175*x4/x5 - 0.03762*sqr(x6)/x5 =L= 1;

e6.. 2462.3121*x2/x3/x4 - 25.125634*x2/x3 + 0.006198*x7 =L= 1;

e7.. 161.18996/x7 + 5000*x2/x3/x7 - 489510*x2/x3/x4/x7 =L= 1;

e8.. 44.333333/x5 + 0.33*x7/x5 =L= 1;

e9..    0.022556*x5 - 0.007595*x7 =L= 1;

e10..  - 0.0005*x1 + 0.00061*x3 =L= 1;

e11.. 0.819672*x1/x3 + 0.819672/x3 =L= 1;

e12.. 24500*x2/x3/x4 - 250*x2/x3 =L= 1;

e13.. 1.2244898e-5*x3/x2*x4 + 0.010204082*x4 =L= 1;

e14.. 6.25e-5*x1*x6 + 6.25e-5*x1 - 7.625E-5*x3 =L= 1;

e15.. 1.22*x3/x1 + 1/x1 - x6 =L= 1;

* set non-default bounds
x1.lo = 1500; x1.up = 2000;
x2.lo = 1; x2.up = 120;
x3.lo = 3000; x3.up = 3500;
x4.lo = 85; x4.up = 93;
x5.lo = 90; x5.up = 95;
x6.lo = 3; x6.up = 12;
x7.lo = 145; x7.up = 162;

Model m / all /;

m.limrow=0; m.limcol=0;
m.tolproj=0.0;

$if NOT '%gams.u1%' == '' $include '%gams.u1%'

$if not set NLP $set NLP NLP
Solve m using %NLP% minimizing objvar;