MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance ex9_2_6

Formatsⓘ	ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)ⓘ	-1. p1 ( gdx sol ) (infeas: 0)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	-1.00000001 (ANTIGONE) -1. (BARON) -1. (COUENNE) -1. (GUROBI) -1. (LINDO) -1. (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. Falk, J E and Liu, J, On Bilevel Programming, Part I: General Nonlinear Cases, Mathematical Programming, 70:1-3, 1995, 47-72.
Sourceⓘ	Test Problem ex9.2.6 of Chapter 9 of Floudas e.a. handbook
Added to libraryⓘ	31 Jul 2001
Problem typeⓘ	QCQP
#Variablesⓘ	16
#Binary Variablesⓘ	0
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	16
#Nonlinear Binary Variablesⓘ	0
#Nonlinear Integer Variablesⓘ	0
Objective Senseⓘ	min
Objective typeⓘ	quadratic
Objective curvatureⓘ	convex
#Nonzeros in Objectiveⓘ	4
#Nonlinear Nonzeros in Objectiveⓘ	4
#Constraintsⓘ	12
#Linear Constraintsⓘ	6
#Quadratic Constraintsⓘ	6
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ
Constraints curvatureⓘ	indefinite
#Nonzeros in Jacobianⓘ	28
#Nonlinear Nonzeros in Jacobianⓘ	12
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	16
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	4
#Blocks in Hessian of Lagrangianⓘ	10
Minimal blocksize in Hessian of Lagrangianⓘ	1
Maximal blocksize in Hessian of Lagrangianⓘ	2
Average blocksize in Hessian of Lagrangianⓘ	1.6
#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ⓘ	1.5
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*         13       13        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
*         33       17       16        0
*
*  Solve m using NLP minimizing objvar;


Variables  objvar,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17;

Positive Variables  x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17;

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


e1.. x2*x2 - 2*x2 + x3*x3 - 2*x3 + x4*x4 + x5*x5 - objvar =E= 0;

e2..  - x4 + x6 =E= -0.5;

e3..  - x5 + x7 =E= -0.5;

e4..    x4 + x8 =E= 1.5;

e5..    x5 + x9 =E= 1.5;

e6.. x6*x12 =E= 0;

e7.. x7*x13 =E= 0;

e8.. x8*x14 =E= 0;

e9.. x9*x15 =E= 0;

e10.. x10*x16 =E= 0;

e11.. x11*x17 =E= 0;

e12..  - 2*x2 + 2*x4 - x12 + x14 =E= 0;

e13..  - 2*x3 + 2*x5 - x13 + x15 =E= 0;

* set non-default bounds
x6.up = 200;
x7.up = 200;
x8.up = 200;
x9.up = 200;
x10.up = 200;
x11.up = 200;
x12.up = 200;
x13.up = 200;
x14.up = 200;
x15.up = 200;
x16.up = 200;
x17.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;