MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance ex3_1_3

Formatsⓘ	ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)ⓘ	-310. p1 ( gdx sol ) (infeas: 0)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	-310.0000003 (ANTIGONE) -310.0001011 (BARON) -310.0000001 (COUENNE) -310. (GUROBI) -310. (LINDO) -310.0000374 (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. Hesse, R, A Heuristic Search Procedure for Estimating a Global Solution of Nonconvex Programming Problems, Operations Research, 21:6, 1973, 1267--1280.
Sourceⓘ	Test Problem ex3.1.3 of Chapter 3 of Floudas e.a. handbook
Added to libraryⓘ	31 Jul 2001
Problem typeⓘ	QCQP
#Variablesⓘ	6
#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ⓘ	concave
#Nonzeros in Objectiveⓘ	6
#Nonlinear Nonzeros in Objectiveⓘ	6
#Constraintsⓘ	6
#Linear Constraintsⓘ	4
#Quadratic Constraintsⓘ	2
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ
Constraints curvatureⓘ	concave
#Nonzeros in Jacobianⓘ	12
#Nonlinear Nonzeros in Jacobianⓘ	2
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	6
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	6
#Blocks in Hessian of Lagrangianⓘ	6
Minimal blocksize in Hessian of Lagrangianⓘ	1
Maximal blocksize in Hessian of Lagrangianⓘ	1
Average blocksize in Hessian of Lagrangianⓘ	1.0
#Semicontinuitiesⓘ	0
#Nonlinear Semicontinuitiesⓘ	0
#SOS type 1ⓘ	0
#SOS type 2ⓘ	0
Minimal coefficientⓘ	1.0000e+00
Maximal coefficientⓘ	2.5000e+01
Infeasibility of initial pointⓘ	0
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*          7        1        3        3        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
*         19       11        8        0
*
*  Solve m using NLP minimizing objvar;


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

Positive Variables  x1,x2,x4,x6;

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


e1.. -(-25*sqr((-2) + x1) - sqr((-2) + x2) - sqr((-1) + x3) - sqr((-4) + x4) - 
     sqr((-1) + x5) - sqr((-4) + x6)) + objvar =E= 0;

e2.. sqr((-3) + x3) + x4 =G= 4;

e3.. sqr((-3) + x5) + x6 =G= 4;

e4..    x1 - 3*x2 =L= 2;

e5..  - x1 + x2 =L= 2;

e6..    x1 + x2 =L= 6;

e7..    x1 + x2 =G= 2;

* set non-default bounds
x3.lo = 1; x3.up = 5;
x4.up = 6;
x5.lo = 1; x5.up = 5;
x6.up = 10;

* set non-default levels
x1.l = 5;
x2.l = 1;
x3.l = 5;
x5.l = 5;
x6.l = 10;

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;