MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

Home // Instances // Documentation // Download // Statistics

Instance ex9_1_8

Formatsⓘ	ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)ⓘ	-3.25 p1 ( gdx sol ) (infeas: 0)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	-3.25 (ANTIGONE) -3.25 (BARON) -3.25 (COUENNE) -3.25 (GUROBI) -3.25 (LINDO) -3.25 (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. Bard, J F and Falk, J E, An Explicit Solution to the Multi-Level Programming Problem, Computers and Operations Research, 9:1, 1982, 77-100.
Sourceⓘ	Test Problem ex9.1.8 of Chapter 9 of Floudas e.a. handbook
Added to libraryⓘ	31 Jul 2001
Problem typeⓘ	QCP
#Variablesⓘ	14
#Binary Variablesⓘ	0
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	10
#Nonlinear Binary Variablesⓘ	0
#Nonlinear Integer Variablesⓘ	0
Objective Senseⓘ	min
Objective typeⓘ	linear
Objective curvatureⓘ	linear
#Nonzeros in Objectiveⓘ	3
#Nonlinear Nonzeros in Objectiveⓘ	0
#Constraintsⓘ	12
#Linear Constraintsⓘ	7
#Quadratic Constraintsⓘ	5
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ
Constraints curvatureⓘ	indefinite
#Nonzeros in Jacobianⓘ	29
#Nonlinear Nonzeros in Jacobianⓘ	10
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	10
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	0
#Blocks in Hessian of Lagrangianⓘ	5
Minimal blocksize in Hessian of Lagrangianⓘ	2
Maximal blocksize in Hessian of Lagrangianⓘ	2
Average blocksize in Hessian of Lagrangianⓘ	2.0
#Semicontinuitiesⓘ	0
#Nonlinear Semicontinuitiesⓘ	0
#SOS type 1ⓘ	0
#SOS type 2ⓘ	0
Minimal coefficientⓘ	5.0000e-01
Maximal coefficientⓘ	3.0000e+00
Infeasibility of initial pointⓘ	4
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*         13       12        0        1        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         15       15        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         33       23       10        0
*
*  Solve m using NLP minimizing objvar;


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

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

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


e1..  - objvar - 2*x2 + x3 + 0.5*x4 =E= 0;

e2..    x2 + x3 =L= 2;

e3..  - 2*x2 + x4 - x5 + x6 =E= -2.5;

e4..    x2 - 3*x3 + x5 + x7 =E= 2;

e5..  - x4 + x8 =E= 0;

e6..  - x5 + x9 =E= 0;

e7.. x11*x6 =E= 0;

e8.. x12*x7 =E= 0;

e9.. x13*x8 =E= 0;

e10.. x14*x9 =E= 0;

e11.. x15*x10 =E= 0;

e12..    x11 - x13 =E= 4;

e13..    x11 + x12 - x14 =E= -1;

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;