MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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

Instance ex9_2_5

Formatsⓘ	ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)ⓘ	5.00000015 p2 ( gdx sol ) (infeas: 9e-16) 9. p1 ( gdx sol ) (infeas: 2e-15)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	-0.00000048 (ANTIGONE) 4.99999999 (BARON) 5. (COUENNE) 5. (GUROBI) 5. (LINDO) 5. (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, Bilevel Programming for Steady-State Chemical Process Design - I. Fundamentals and Algorithms, Computers and Chemical Engineering, 14:1, 1990, 87-97.
Sourceⓘ	Test Problem ex9.2.5 of Chapter 9 of Floudas e.a. handbook
Added to libraryⓘ	31 Jul 2001
Problem typeⓘ	QCQP
#Variablesⓘ	8
#Binary Variablesⓘ	0
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	8
#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ⓘ	7
#Linear Constraintsⓘ	4
#Quadratic Constraintsⓘ	3
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ
Constraints curvatureⓘ	indefinite
#Nonzeros in Jacobianⓘ	19
#Nonlinear Nonzeros in Jacobianⓘ	6
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	8
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	2
#Blocks in Hessian of Lagrangianⓘ	5
Minimal blocksize in Hessian of Lagrangianⓘ	1
Maximal blocksize in Hessian of Lagrangianⓘ	2
Average blocksize in Hessian of Lagrangianⓘ	1.6
#Semicontinuitiesⓘ	0
#Nonlinear Semicontinuitiesⓘ	0
#SOS type 1ⓘ	0
#SOS type 2ⓘ	0
Minimal coefficientⓘ	1.0000e+00
Maximal coefficientⓘ	3.0000e+00
Infeasibility of initial pointⓘ	14
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*          8        8        0        0        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*          9        9        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         22       14        8        0
*
*  Solve m using NLP minimizing objvar;


Variables  x1,objvar,x3,x4,x5,x6,x7,x8,x9;

Positive Variables  x3,x4,x5,x6,x7,x8,x9;

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


e1.. (-3 + x3)*(-3 + x3) + (-2 + x1)*(-2 + x1) - objvar =E= 0;

e2..    x1 - 2*x3 + x4 =E= 1;

e3..  - 2*x1 + x3 + x5 =E= 2;

e4..    2*x1 + x3 + x6 =E= 14;

e5.. x4*x7 =E= 0;

e6.. x5*x8 =E= 0;

e7.. x6*x9 =E= 0;

e8..    2*x1 + x7 - 2*x8 + 2*x9 =E= 10;

* set non-default bounds
x3.up = 8;

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;