MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance ex14_1_5

Formatsⓘ	ams gms mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)ⓘ	-0.00000000 p1 ( gdx sol ) (infeas: 6e-14)
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. Kearfott, R and Novoa, M, Algorithm 681: INTBIS, A Portable Interval Newton/Bisection Package, ACM Transactions on Mathematical Software, 16:2, 1990, 152-157.
Sourceⓘ	Test Problem ex14.1.5 of Chapter 14 of Floudas e.a. handbook
Added to libraryⓘ	31 Jul 2001
Problem typeⓘ	NLP
#Variablesⓘ	6
#Binary Variablesⓘ	0
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	5
#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ⓘ	6
#Linear Constraintsⓘ	4
#Quadratic Constraintsⓘ	0
#Polynomial Constraintsⓘ	2
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ
Constraints curvatureⓘ	indefinite
#Nonzeros in Jacobianⓘ	32
#Nonlinear Nonzeros in Jacobianⓘ	10
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	20
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	0
#Blocks in Hessian of Lagrangianⓘ	1
Minimal blocksize in Hessian of Lagrangianⓘ	5
Maximal blocksize in Hessian of Lagrangianⓘ	5
Average blocksize in Hessian of Lagrangianⓘ	5.0
#Semicontinuitiesⓘ	0
#Nonlinear Semicontinuitiesⓘ	0
#SOS type 1ⓘ	0
#SOS type 2ⓘ	0
Minimal coefficientⓘ	1.0000e+00
Maximal coefficientⓘ	2.0000e+00
Infeasibility of initial pointⓘ	6
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*          7        5        0        2        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*          7        7        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         34       24       10        0
*
*  Solve m using NLP minimizing objvar;


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

Equations  e1,e2,e3,e4,e5,e6,e7;


e1..  - x6 + objvar =E= 0;

e2..    2*x1 + x2 + x3 + x4 + x5 =E= 6;

e3..    x1 + 2*x2 + x3 + x4 + x5 =E= 6;

e4..    x1 + x2 + 2*x3 + x4 + x5 =E= 6;

e5..    x1 + x2 + x3 + 2*x4 + x5 =E= 6;

e6.. x1*x2*x3*x4*x5 - x6 =L= 1;

e7.. -x1*x2*x3*x4*x5 - x6 =L= -1;

* set non-default bounds
x1.lo = -2; x1.up = 2;
x2.lo = -2; x2.up = 2;
x3.lo = -2; x3.up = 2;
x4.lo = -2; x4.up = 2;
x5.lo = -2; x5.up = 2;

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;