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Instance ex5_4_4

Formatsⓘ	ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)ⓘ	11841.60921000 p1 ( gdx sol ) (infeas: 0) 10077.77540000 p2 ( gdx sol ) (infeas: 0)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	10077.77537000 (ANTIGONE) 10077.77539000 (BARON) 10077.77540000 (COUENNE) 10077.77539000 (LINDO) 10077.77540000 (SCIP) 1691.75984800 (SHOT)
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. Floudas, C A and Ciric, A R, Eds, Proceedings of the Third International Symposium on Process Systems Engineering, 1988.
Sourceⓘ	Test Problem ex5.4.4 of Chapter 5 of Floudas e.a. handbook
Added to libraryⓘ	31 Jul 2001
Problem typeⓘ	NLP
#Variablesⓘ	27
#Binary Variablesⓘ	0
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	21
#Nonlinear Binary Variablesⓘ	0
#Nonlinear Integer Variablesⓘ	0
Objective Senseⓘ	min
Objective typeⓘ	nonlinear
Objective curvatureⓘ	nonconcave
#Nonzeros in Objectiveⓘ	6
#Nonlinear Nonzeros in Objectiveⓘ	6
#Constraintsⓘ	19
#Linear Constraintsⓘ	13
#Quadratic Constraintsⓘ	6
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ	div mul vcpower
Constraints curvatureⓘ	indefinite
#Nonzeros in Jacobianⓘ	69
#Nonlinear Nonzeros in Jacobianⓘ	27
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	36
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	6
#Blocks in Hessian of Lagrangianⓘ	6
Minimal blocksize in Hessian of Lagrangianⓘ	2
Maximal blocksize in Hessian of Lagrangianⓘ	5
Average blocksize in Hessian of Lagrangianⓘ	3.5
#Semicontinuitiesⓘ	0
#Nonlinear Semicontinuitiesⓘ	0
#SOS type 1ⓘ	0
#SOS type 2ⓘ	0
Minimal coefficientⓘ	1.6667e-01
Maximal coefficientⓘ	2.0000e+03
Infeasibility of initial pointⓘ	2000
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*         20       20        0        0        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         28       28        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         76       43       33        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,x18,x19
          ,x20,x21,x22,x23,x24,x25,x26,x27,objvar;

Positive Variables  x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17,x18,x19,x20,x21;

Equations  e1,e2,e3,e4,e5,e6,e7,e8,e9,e10,e11,e12,e13,e14,e15,e16,e17,e18,e19
          ,e20;


e1..    x7 + x12 + x17 =E= 45;

e2..    x7 - x8 + x14 + x20 =E= 0;

e3..    x9 + x12 - x13 + x19 =E= 0;

e4..    x10 + x15 + x17 - x18 =E= 0;

e5..  - x8 + x9 + x10 + x11 =E= 0;

e6..  - x13 + x14 + x15 + x16 =E= 0;

e7..  - x18 + x19 + x20 + x21 =E= 0;

e8.. x25*x14 + x27*x20 - x22*x8 + 100*x7 =E= 0;

e9.. x23*x9 + x27*x19 - x24*x13 + 100*x12 =E= 0;

e10.. x23*x10 + x25*x15 - x26*x18 + 100*x17 =E= 0;

e11.. x8*x23 - x8*x22 =E= 2000;

e12.. x13*x25 - x13*x24 =E= 1000;

e13.. x18*x27 - x18*x26 =E= 1500;

e14..    x1 + x23 =E= 210;

e15..    x2 + x22 =E= 130;

e16..    x3 + x25 =E= 210;

e17..    x4 + x24 =E= 160;

e18..    x5 + x27 =E= 210;

e19..    x6 + x26 =E= 180;

e20.. -(1300*(2000/(0.333333333333333*x1*x2 + 0.166666666666667*x1 + 
      0.166666666666667*x2))**0.6 + 1300*(1000/(0.666666666666667*x3*x4 + 
      0.166666666666667*x3 + 0.166666666666667*x4))**0.6 + 1300*(1500/(
      0.666666666666667*x5*x6 + 0.166666666666667*x5 + 0.166666666666667*x6))**
      0.6) + objvar =E= 0;

* set non-default bounds
x1.lo = 10; x1.up = 110;
x2.lo = 10; x2.up = 110;
x3.lo = 10; x3.up = 110;
x4.lo = 10; x4.up = 110;
x5.lo = 10; x5.up = 110;
x6.lo = 10; x6.up = 110;
x7.up = 45;
x8.up = 45;
x9.up = 45;
x10.up = 45;
x11.up = 45;
x12.up = 45;
x13.up = 45;
x14.up = 45;
x15.up = 45;
x16.up = 45;
x17.up = 45;
x18.up = 45;
x19.up = 45;
x20.up = 45;
x21.up = 45;
x22.lo = 100; x22.up = 200;
x23.lo = 100; x23.up = 200;
x24.lo = 100; x24.up = 200;
x25.lo = 100; x25.up = 200;
x26.lo = 100; x26.up = 200;
x27.lo = 100; x27.up = 200;

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;