MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance ex7_3_3

Formatsⓘ	ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)ⓘ	1.14477980 p1 ( gdx sol ) (infeas: 2e-15) 0.81752905 p2 ( gdx sol ) (infeas: 1e-14)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	0.81752905 (ANTIGONE) 0.81752905 (BARON) 0.81752905 (COUENNE) 0.81752903 (GUROBI) 0.81752905 (LINDO) 0.81752903 (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. Ackermann, J, Kaesbauer, D, and Muench, R, Robust Gamma-Stability Analysis in a Plant Parameter Space, Automatica, 27:1, 1991, 75-85.
Sourceⓘ	Test Problem ex7.3.3 of Chapter 7 of Floudas e.a. handbook
Added to libraryⓘ	31 Jul 2001
Problem typeⓘ	QCP
#Variablesⓘ	5
#Binary Variablesⓘ	0
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	3
#Nonlinear Binary Variablesⓘ	0
#Nonlinear Integer Variablesⓘ	0
Objective Senseⓘ	min
Objective typeⓘ	linear
Objective curvatureⓘ	linear
#Nonzeros in Objectiveⓘ	1
#Nonlinear Nonzeros in Objectiveⓘ	0
#Constraintsⓘ	8
#Linear Constraintsⓘ	6
#Quadratic Constraintsⓘ	2
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ
Constraints curvatureⓘ	indefinite
#Nonzeros in Jacobianⓘ	20
#Nonlinear Nonzeros in Jacobianⓘ	5
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	5
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	1
#Blocks in Hessian of Lagrangianⓘ	1
Minimal blocksize in Hessian of Lagrangianⓘ	3
Maximal blocksize in Hessian of Lagrangianⓘ	3
Average blocksize in Hessian of Lagrangianⓘ	3.0
#Semicontinuitiesⓘ	0
#Nonlinear Semicontinuitiesⓘ	0
#SOS type 1ⓘ	0
#SOS type 2ⓘ	0
Minimal coefficientⓘ	2.5000e-01
Maximal coefficientⓘ	7.8000e+01
Infeasibility of initial pointⓘ	44
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*          9        3        0        6        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*          6        6        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         22       17        5        0
*
*  Solve m using NLP minimizing objvar;


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

Positive Variables  x4;

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


e1..  - x5 + objvar =E= 0;

e2.. 9.625*x1*x4 - 4*x1 - 78*x4 + 16*x2*x4 - x2 + 16*sqr(x4) + x3 =E= -12;

e3.. 16*x1*x4 - 19*x1 - 24*x4 - 8*x2 - x3 =E= -44;

e4..    x1 - 0.25*x5 =L= 2.25;

e5..  - x1 - 0.25*x5 =L= -2.25;

e6..  - x2 - 0.5*x5 =L= -1.5;

e7..    x2 - 0.5*x5 =L= 1.5;

e8..  - x3 - 1.5*x5 =L= -1.5;

e9..    x3 - 1.5*x5 =L= 1.5;

* set non-default bounds
x4.up = 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;