MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance ex9_1_4

Formatsⓘ	ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)ⓘ	-37.00000000 p1 ( gdx sol ) (infeas: 4e-15)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	-37.00000004 (ANTIGONE) -37.00000000 (BARON) -37.00000000 (COUENNE) -37.00000000 (GUROBI) -37.00000000 (LINDO) -37.00000000 (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. Clark, P A and Westerberg, A W, A Note on the Optimality Conditions for the Bilevel Programming Problem, Naval Research Logistics, 35, 1988, 413-418.
Sourceⓘ	Test Problem ex9.1.4 of Chapter 9 of Floudas e.a. handbook
Added to libraryⓘ	31 Jul 2001
Problem typeⓘ	QCP
#Variablesⓘ	10
#Binary Variablesⓘ	0
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	8
#Nonlinear Binary Variablesⓘ	0
#Nonlinear Integer Variablesⓘ	0
Objective Senseⓘ	min
Objective typeⓘ	linear
Objective curvatureⓘ	linear
#Nonzeros in Objectiveⓘ	2
#Nonlinear Nonzeros in Objectiveⓘ	0
#Constraintsⓘ	9
#Linear Constraintsⓘ	5
#Quadratic Constraintsⓘ	4
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ
Constraints curvatureⓘ	indefinite
#Nonzeros in Jacobianⓘ	23
#Nonlinear Nonzeros in Jacobianⓘ	8
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	8
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	0
#Blocks in Hessian of Lagrangianⓘ	4
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ⓘ	1.0000e+00
Maximal coefficientⓘ	5.0000e+00
Infeasibility of initial pointⓘ	108
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*         10       10        0        0        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
*         26       18        8        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;


e1..  - objvar + x2 - 4*x3 =E= 0;

e2..  - 2*x2 + x3 + x4 =E= 0;

e3..    2*x2 + 5*x3 + x5 =E= 108;

e4..    2*x2 - 3*x3 + x6 =E= -4;

e5..  - x3 + x7 =E= 0;

e6.. x8*x4 =E= 0;

e7.. x9*x5 =E= 0;

e8.. x10*x6 =E= 0;

e9.. x11*x7 =E= 0;

e10..    x8 + 5*x9 - 3*x10 - x11 =E= -1;

* set non-default bounds
x4.up = 200;
x5.up = 200;
x6.up = 200;
x7.up = 200;
x8.up = 200;
x9.up = 200;
x10.up = 200;
x11.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;