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Instance ex14_1_7

Formatsⓘ	ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)ⓘ	7.04274947 p1 ( gdx sol ) (infeas: 3e-14) 0.13499021 p2 ( gdx sol ) (infeas: 1e-14) 0.00000000 p3 ( gdx sol ) (infeas: 2e-13)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	-0.00000000 (ANTIGONE) 0.00000000 (BARON) -0.00000000 (COUENNE) -0.00000000 (LINDO) 0.00000000 (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. Ratschek, H and Rokne, J, Experiments using interval analysis for solving a circuit design problem, Journal of Global Optimization, 3:4, 1993, 501-518.
Sourceⓘ	Test Problem ex14.1.7 of Chapter 14 of Floudas e.a. handbook
Added to libraryⓘ	31 Jul 2001
Problem typeⓘ	NLP
#Variablesⓘ	10
#Binary Variablesⓘ	0
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	9
#Nonlinear Binary Variablesⓘ	0
#Nonlinear Integer Variablesⓘ	0
Objective Senseⓘ	min
Objective typeⓘ	linear
Objective curvatureⓘ	linear
#Nonzeros in Objectiveⓘ	1
#Nonlinear Nonzeros in Objectiveⓘ	0
#Constraintsⓘ	17
#Linear Constraintsⓘ	0
#Quadratic Constraintsⓘ	1
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	16
Operands in Gen. Nonlin. Functionsⓘ	exp mul
Constraints curvatureⓘ	indefinite
#Nonzeros in Jacobianⓘ	116
#Nonlinear Nonzeros in Jacobianⓘ	100
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	59
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	5
#Blocks in Hessian of Lagrangianⓘ	1
Minimal blocksize in Hessian of Lagrangianⓘ	9
Maximal blocksize in Hessian of Lagrangianⓘ	9
Average blocksize in Hessian of Lagrangianⓘ	9.0
#Semicontinuitiesⓘ	0
#Nonlinear Semicontinuitiesⓘ	0
#SOS type 1ⓘ	0
#SOS type 2ⓘ	0
Minimal coefficientⓘ	5.2095e-03
Maximal coefficientⓘ	2.1148e+02
Infeasibility of initial pointⓘ	211.5
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*         18        2        0       16        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         11       11        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        118       18      100        0
*
*  Solve m using NLP minimizing objvar;


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

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

Equations  e1,e2,e3,e4,e5,e6,e7,e8,e9,e10,e11,e12,e13,e14,e15,e16,e17,e18;


e1..  - x10 + objvar =E= 0;

e2.. (1 - x1*x2)*x3*(-1 + exp(x5*(0.485 - 0.0052095*x7 - 0.0285132*x8))) + 
     23.3037*x2 - x10 =L= 28.5132;

e3.. (1 - x1*x2)*x3*(-1 + exp(x5*(0.752 - 0.0100677*x7 - 0.1118467*x8))) + 
     101.779*x2 - x10 =L= 111.8467;

e4.. (1 - x1*x2)*x3*(-1 + exp(x5*(0.869 - 0.0229274*x7 - 0.1343884*x8))) + 
     111.461*x2 - x10 =L= 134.3884;

e5.. (1 - x1*x2)*x3*(-1 + exp(x5*(0.982 - 0.0202153*x7 - 0.2114823*x8))) + 
     191.267*x2 - x10 =L= 211.4823;

e6.. (-(1 - x1*x2)*x3*(-1 + exp(x5*(0.485 - 0.0052095*x7 - 0.0285132*x8)))) - 
     23.3037*x2 - x10 =L= -28.5132;

e7.. (-(1 - x1*x2)*x3*(-1 + exp(x5*(0.752 - 0.0100677*x7 - 0.1118467*x8)))) - 
     101.779*x2 - x10 =L= -111.8467;

e8.. (-(1 - x1*x2)*x3*(-1 + exp(x5*(0.869 - 0.0229274*x7 - 0.1343884*x8)))) - 
     111.461*x2 - x10 =L= -134.3884;

e9.. (-(1 - x1*x2)*x3*(-1 + exp(x5*(0.982 - 0.0202153*x7 - 0.2114823*x8)))) - 
     191.267*x2 - x10 =L= -211.4823;

e10.. (1 - x1*x2)*x4*(-1 + exp(x6*(0.116 - 0.0052095*x7 + 0.0233037*x9))) - 
      28.5132*x1 - x10 =L= -23.3037;

e11.. (1 - x1*x2)*x4*(-1 + exp(x6*(-0.502 - 0.0100677*x7 + 0.101779*x9))) - 
      111.8467*x1 - x10 =L= -101.779;

e12.. (1 - x1*x2)*x4*(-1 + exp(x6*(0.166 - 0.0229274*x7 + 0.111461*x9))) - 
      134.3884*x1 - x10 =L= -111.461;

e13.. (1 - x1*x2)*x4*(-1 + exp(x6*(-0.473 - 0.0202153*x7 + 0.191267*x9))) - 
      211.4823*x1 - x10 =L= -191.267;

e14.. 28.5132*x1 - (1 - x1*x2)*x4*(-1 + exp(x6*(0.116 - 0.0052095*x7 + 
      0.0233037*x9))) - x10 =L= 23.3037;

e15.. 111.8467*x1 - (1 - x1*x2)*x4*(-1 + exp(x6*(-0.502 - 0.0100677*x7 + 
      0.101779*x9))) - x10 =L= 101.779;

e16.. 134.3884*x1 - (1 - x1*x2)*x4*(-1 + exp(x6*(0.166 - 0.0229274*x7 + 
      0.111461*x9))) - x10 =L= 111.461;

e17.. 211.4823*x1 - (1 - x1*x2)*x4*(-1 + exp(x6*(-0.473 - 0.0202153*x7 + 
      0.191267*x9))) - x10 =L= 191.267;

e18.. x1*x3 - x2*x4 =E= 0;

* set non-default bounds
x1.up = 10;
x2.up = 10;
x3.up = 10;
x4.up = 10;
x5.up = 10;
x6.up = 10;
x7.up = 10;
x8.up = 10;
x9.up = 10;

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;