MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance ex9_2_4

Formatsⓘ	ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)ⓘ	0.5 p1 ( gdx sol ) (infeas: 0)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	0.5 (ANTIGONE) 0.5 (BARON) 0.5 (COUENNE) 0.5 (GUROBI) 0.5 (LINDO) 0.5 (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. Yezza, A, First-Order Necessary Optimality Conditions for General Bilevel Programming Problems, Journal of Optimization Theory and Applications, 89:1, 1996, 189-219.
Sourceⓘ	Test Problem ex9.2.4 of Chapter 9 of Floudas e.a. handbook
Added to libraryⓘ	31 Jul 2001
Problem typeⓘ	QCQP
#Variablesⓘ	8
#Binary Variablesⓘ	0
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	6
#Nonlinear Binary Variablesⓘ	0
#Nonlinear Integer Variablesⓘ	0
Objective Senseⓘ	min
Objective typeⓘ	quadratic
Objective curvatureⓘ	convex
#Nonzeros in Objectiveⓘ	2
#Nonlinear Nonzeros in Objectiveⓘ	2
#Constraintsⓘ	7
#Linear Constraintsⓘ	5
#Quadratic Constraintsⓘ	2
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ
Constraints curvatureⓘ	indefinite
#Nonzeros in Jacobianⓘ	16
#Nonlinear Nonzeros in Jacobianⓘ	4
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	6
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	2
#Blocks in Hessian of Lagrangianⓘ	4
Minimal blocksize in Hessian of Lagrangianⓘ	1
Maximal blocksize in Hessian of Lagrangianⓘ	2
Average blocksize in Hessian of Lagrangianⓘ	1.5
#Semicontinuitiesⓘ	0
#Nonlinear Semicontinuitiesⓘ	0
#SOS type 1ⓘ	0
#SOS type 2ⓘ	0
Minimal coefficientⓘ	5.0000e-01
Maximal coefficientⓘ	2.0000e+00
Infeasibility of initial pointⓘ	1
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*          8        8        0        0        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*          9        9        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         19       13        6        0
*
*  Solve m using NLP minimizing objvar;


Variables  objvar,x2,x3,x4,x5,x6,x7,x8,x9;

Positive Variables  x3,x4,x5,x6,x7,x8,x9;

Equations  e1,e2,e3,e4,e5,e6,e7,e8;


e1.. (-1 + 0.5*x4)*(-2 + x4) + (-1 + 0.5*x5)*(-2 + x5) - objvar =E= 0;

e2..  - x3 + x4 + x5 =E= 0;

e3..  - x4 + x6 =E= 0;

e4..  - x5 + x7 =E= 0;

e5.. x6*x8 =E= 0;

e6.. x7*x9 =E= 0;

e7..    x2 + x4 - x8 =E= 0;

e8..    x2 - x9 =E= -1;

* set non-default bounds
x6.up = 200;
x7.up = 200;
x8.up = 200;
x9.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;