MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance ex2_1_9

Formatsⓘ	ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)ⓘ	-0.375 p1 ( gdx sol ) (infeas: 0)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	-0.375 (ANTIGONE) -0.375 (BARON) -0.375 (COUENNE) -0.375 (CPLEX) -0.3750014 (GUROBI) -0.375 (LINDO) -0.375 (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.
Sourceⓘ	Test Problem ex2.1.9 of Chapter 2 of Floudas e.a. handbook
Added to libraryⓘ	31 Jul 2001
Problem typeⓘ	QP
#Variablesⓘ	10
#Binary Variablesⓘ	0
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	10
#Nonlinear Binary Variablesⓘ	0
#Nonlinear Integer Variablesⓘ	0
Objective Senseⓘ	min
Objective typeⓘ	quadratic
Objective curvatureⓘ	indefinite
#Nonzeros in Objectiveⓘ	10
#Nonlinear Nonzeros in Objectiveⓘ	10
#Constraintsⓘ	1
#Linear Constraintsⓘ	1
#Quadratic Constraintsⓘ	0
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ
Constraints curvatureⓘ	linear
#Nonzeros in Jacobianⓘ	10
#Nonlinear Nonzeros in Jacobianⓘ	0
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	44
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	0
#Blocks in Hessian of Lagrangianⓘ	1
Minimal blocksize in Hessian of Lagrangianⓘ	10
Maximal blocksize in Hessian of Lagrangianⓘ	10
Average blocksize in Hessian of Lagrangianⓘ	10.0
#Semicontinuitiesⓘ	0
#Nonlinear Semicontinuitiesⓘ	0
#SOS type 1ⓘ	0
#SOS type 2ⓘ	0
Minimal coefficientⓘ	1.0000e+00
Maximal coefficientⓘ	1.0000e+00
Infeasibility of initial pointⓘ	0
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*          2        2        0        0        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
*         21       11       10        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,x10;

Equations  e1,e2;


e1.. -(x1*x2 + x2*x3 + x3*x4 + x4*x5 + x5*x6 + x6*x7 + x7*x8 + x8*x9 + x9*x10
      + x1*x3 + x2*x4 + x3*x5 + x4*x6 + x5*x7 + x6*x8 + x7*x9 + x8*x10 + x1*x9
      + x1*x10 + x2*x10 + x1*x5 + x4*x7) - objvar =E= 0;

e2..    x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9 + x10 =E= 1;

* set non-default levels
x4.l = 0.25;
x5.l = 0.25;
x6.l = 0.25;
x7.l = 0.25;

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;