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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance ex5_4_3

Formatsⓘ	ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)ⓘ	4845.46200500 p1 ( gdx sol ) (infeas: 5e-13)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	4845.46200000 (ANTIGONE) 4845.46199600 (BARON) 4845.46200500 (COUENNE) 4845.46200400 (LINDO) 4845.46200500 (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. Visweswaran, V and Floudas, C A, Computational Results for an Efficient Implementation of the GOP Algorithm and its Variants. Chapter 4 in Grossmann, I E, Ed, Global Optimization in Engineering Design, Kluwer Books, 1996, 111-153.
Sourceⓘ	Test Problem ex5.4.3 of Chapter 5 of Floudas e.a. handbook
Added to libraryⓘ	31 Jul 2001
Problem typeⓘ	NLP
#Variablesⓘ	16
#Binary Variablesⓘ	0
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	12
#Nonlinear Binary Variablesⓘ	0
#Nonlinear Integer Variablesⓘ	0
Objective Senseⓘ	min
Objective typeⓘ	nonlinear
Objective curvatureⓘ	nonconcave
#Nonzeros in Objectiveⓘ	4
#Nonlinear Nonzeros in Objectiveⓘ	4
#Constraintsⓘ	13
#Linear Constraintsⓘ	9
#Quadratic Constraintsⓘ	4
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ	div mul vcpower
Constraints curvatureⓘ	indefinite
#Nonzeros in Jacobianⓘ	38
#Nonlinear Nonzeros in Jacobianⓘ	14
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	20
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	4
#Blocks in Hessian of Lagrangianⓘ	4
Minimal blocksize in Hessian of Lagrangianⓘ	2
Maximal blocksize in Hessian of Lagrangianⓘ	4
Average blocksize in Hessian of Lagrangianⓘ	3.0
#Semicontinuitiesⓘ	0
#Nonlinear Semicontinuitiesⓘ	0
#SOS type 1ⓘ	0
#SOS type 2ⓘ	0
Minimal coefficientⓘ	3.3333e-02
Maximal coefficientⓘ	1.3000e+03
Infeasibility of initial pointⓘ	1000
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*         14       14        0        0        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         17       17        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         43       25       18        0
*
*  Solve m using NLP minimizing objvar;


Variables  x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,objvar;

Positive Variables  x5,x6,x7,x8,x9,x10,x11,x12;

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


e1..    x5 + x9 =E= 10;

e2..    x5 - x6 + x11 =E= 0;

e3..    x7 + x9 - x10 =E= 0;

e4..  - x6 + x7 + x8 =E= 0;

e5..  - x10 + x11 + x12 =E= 0;

e6.. x16*x11 - x13*x6 + 150*x5 =E= 0;

e7.. x15*x7 - x14*x10 + 150*x9 =E= 0;

e8.. x6*x15 - x6*x13 =E= 1000;

e9.. x10*x16 - x10*x14 =E= 600;

e10..    x1 + x15 =E= 500;

e11..    x2 + x13 =E= 250;

e12..    x3 + x16 =E= 350;

e13..    x4 + x14 =E= 200;

e14.. -(1300*(1000/(0.0333333333333333*x1*x2 + 0.166666666666667*x1 + 
      0.166666666666667*x2))**0.6 + 1300*(600/(0.0333333333333333*x3*x4 + 
      0.166666666666667*x3 + 0.166666666666667*x4))**0.6) + objvar =E= 0;

* set non-default bounds
x1.lo = 10; x1.up = 350;
x2.lo = 10; x2.up = 350;
x3.lo = 10; x3.up = 200;
x4.lo = 10; x4.up = 200;
x5.up = 10;
x6.up = 10;
x7.up = 10;
x8.up = 10;
x9.up = 10;
x10.up = 10;
x11.up = 10;
x12.up = 10;
x13.lo = 150; x13.up = 310;
x14.lo = 150; x14.up = 310;
x15.lo = 150; x15.up = 310;
x16.lo = 150; x16.up = 310;

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;