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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance ex7_3_5

Formatsⓘ	ams gms mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)ⓘ	1.20689655 p1 ( gdx sol ) (infeas: 0) 1.20687334 p2 ( gdx sol ) (infeas: 3e-10) 1.20687143 p3 ( gdx sol ) (infeas: 4e-10)
Other points (infeas > 1e-08)ⓘ	1.20551050 p4 ( gdx sol ) (infeas: 9e-07) 1.20545316 p5 ( gdx sol ) (infeas: 1e-06)
Dual Boundsⓘ	1.20687143 (ANTIGONE) 1.20665305 (BARON) 1.20652509 (COUENNE) 1.20545316 (GUROBI) 1.20669187 (LINDO) 1.20569526 (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. Ackermann, J, Kaesbauer, D, and Muench, R, Robust Gamma-Stability Analysis in a Plant Parameter Space, Automatica, 27:1, 1991, 75-85.
Sourceⓘ	Test Problem ex7.3.5 of Chapter 7 of Floudas e.a. handbook
Added to libraryⓘ	31 Jul 2001
Problem typeⓘ	NLP
#Variablesⓘ	13
#Binary Variablesⓘ	0
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	10
#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ⓘ	15
#Linear Constraintsⓘ	4
#Quadratic Constraintsⓘ	2
#Polynomial Constraintsⓘ	9
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ
Constraints curvatureⓘ	indefinite
#Nonzeros in Jacobianⓘ	44
#Nonlinear Nonzeros in Jacobianⓘ	25
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	19
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	3
#Blocks in Hessian of Lagrangianⓘ	2
Minimal blocksize in Hessian of Lagrangianⓘ	2
Maximal blocksize in Hessian of Lagrangianⓘ	8
Average blocksize in Hessian of Lagrangianⓘ	5.0
#Semicontinuitiesⓘ	0
#Nonlinear Semicontinuitiesⓘ	0
#SOS type 1ⓘ	0
#SOS type 2ⓘ	0
Minimal coefficientⓘ	1.0800e-05
Maximal coefficientⓘ	8.0000e+00
Infeasibility of initial pointⓘ	0.2
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*         16       12        0        4        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         14       14        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         46       21       25        0
*
*  Solve m using NLP minimizing objvar;


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

Positive Variables  x3;

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


e1..  - x4 + objvar =E= 0;

e2.. POWER(x3,8)*x13 - POWER(x3,6)*x11 + POWER(x3,4)*x9 - sqr(x3)*x7 + x5 =E= 0
     ;

e3.. POWER(x3,6)*x12 - POWER(x3,4)*x10 + sqr(x3)*x8 - x6 =E= 0;

e4..  - x1 - 0.145*x4 =L= -0.175;

e5..    x1 - 0.145*x4 =L= 0.175;

e6..  - x2 - 0.15*x4 =L= -0.2;

e7..    x2 - 0.15*x4 =L= 0.2;

e8.. -4.53*sqr(x1) + x5 =E= 0;

e9.. -(5.28*sqr(x1) + 0.364*x1) + x6 =E= 0;

e10.. -(5.72*sqr(x1)*x2 + 1.13*sqr(x1) + 0.425*x1) + x7 =E= 0;

e11.. -(6.93*sqr(x1)*x2 + 0.0911*x1) + x8 =E= 0.00422;

e12.. -(1.45*sqr(x1)*x2 + 0.168*x1*x2) + x9 =E= 0.000338;

e13.. -(1.56*sqr(x1)*sqr(x2) + 0.00084*sqr(x1)*x2 + 0.0135*x1*x2) + x10
       =E= 1.35E-5;

e14.. -(0.125*sqr(x1)*sqr(x2) + 1.68e-5*sqr(x1)*x2 + 0.000539*x1*x2) + x11
       =E= 2.7E-7;

e15.. -(0.005*sqr(x1)*sqr(x2) + 1.08e-5*x1*x2) + x12 =E= 0;

e16.. -0.0001*sqr(x1)*sqr(x2) + x13 =E= 0;

* set non-default bounds
x3.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;