MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance ex9_2_2

Formatsⓘ	ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)ⓘ	99.99996939 p1 ( gdx sol ) (infeas: 3e-11)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	99.99992444 (ANTIGONE) 99.99996919 (BARON) 99.99996939 (COUENNE) 99.99996939 (GUROBI) 99.99996939 (LINDO) 99.99996939 (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. Shimizu, K and Aiyoshi, E, A New Computational Method for Stackelberg and Min-Max Problems by Use of a Penalty Method, IEEE Transactions on Automatic Control, 26:2, 1981, 460-466.
Sourceⓘ	Test Problem ex9.2.2 of Chapter 9 of Floudas e.a. handbook
Added to libraryⓘ	31 Jul 2001
Problem typeⓘ	QCQP
#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ⓘ	convex
#Nonzeros in Objectiveⓘ	2
#Nonlinear Nonzeros in Objectiveⓘ	2
#Constraintsⓘ	11
#Linear Constraintsⓘ	7
#Quadratic Constraintsⓘ	4
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ
Constraints curvatureⓘ	indefinite
#Nonzeros in Jacobianⓘ	24
#Nonlinear Nonzeros in Jacobianⓘ	8
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	10
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	2
#Blocks in Hessian of Lagrangianⓘ	6
Minimal blocksize in Hessian of Lagrangianⓘ	1
Maximal blocksize in Hessian of Lagrangianⓘ	2
Average blocksize in Hessian of Lagrangianⓘ	1.666667
#Semicontinuitiesⓘ	0
#Nonlinear Semicontinuitiesⓘ	0
#SOS type 1ⓘ	0
#SOS type 2ⓘ	0
Minimal coefficientⓘ	1.0000e+00
Maximal coefficientⓘ	1.0000e+01
Infeasibility of initial pointⓘ	60
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*         12        9        0        3        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
*         27       17       10        0
*
*  Solve m using NLP minimizing objvar;


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

Positive Variables  x2,x3,x4,x5,x6,x7,x8,x9,x10,x11;

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


e1.. x2*x2 + (-10 + x3)*(-10 + x3) - objvar =E= 0;

e2..    x2 =L= 15;

e3..  - x2 + x3 =L= 0;

e4..  - x2 =L= 0;

e5..    x2 + x3 + x4 =E= 20;

e6..  - x3 + x5 =E= 0;

e7..    x3 + x6 =E= 20;

e8.. x4*x8 =E= 0;

e9.. x5*x9 =E= 0;

e10.. x6*x10 =E= 0;

e11.. x7*x11 =E= 0;

e12..    2*x2 + 4*x3 + x8 - x9 + x10 =E= 60;

* set non-default bounds
x4.up = 20;
x5.up = 20;
x6.up = 20;
x7.up = 20;
x8.up = 20;
x9.up = 20;
x10.up = 20;
x11.up = 20;

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;