MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance ex9_1_1

Formatsⓘ	ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)ⓘ	-13.00000000 p1 ( gdx sol ) (infeas: 0)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	-13.00000001 (ANTIGONE) -13.00000000 (BARON) -13.00000000 (COUENNE) -13.00000000 (GUROBI) -13.00000000 (LINDO) -13.00000000 (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, Bilevel Programming for Steady-State Chemical Process Design - I. Fundamentals and Algorithms, Computers and Chemical Engineering, 14:1, 1990, 87-97.
Sourceⓘ	Test Problem ex9.1.1 of Chapter 9 of Floudas e.a. handbook
Added to libraryⓘ	31 Jul 2001
Problem typeⓘ	QCP
#Variablesⓘ	13
#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ⓘ	33
#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ⓘ	1.0000e+00
Maximal coefficientⓘ	8.0000e+00
Infeasibility of initial pointⓘ	48
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*         13       13        0        0        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         14       14        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         37       27       10        0
*
*  Solve m using NLP minimizing objvar;


Variables  x1,x2,objvar,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14;

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

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


e1..  - 3*x1 + 2*x2 - objvar - x4 =E= 0;

e2..    x1 + 4*x2 - 2*x4 + x5 =E= 16;

e3..    3*x1 - 2*x2 + 8*x4 + x6 =E= 48;

e4..    x1 - 3*x2 - 2*x4 + x7 =E= -12;

e5..  - x1 + x8 =E= 0;

e6..    x1 + x9 =E= 4;

e7.. x10*x5 =E= 0;

e8.. x11*x6 =E= 0;

e9.. x12*x7 =E= 0;

e10.. x13*x8 =E= 0;

e11.. x14*x9 =E= 0;

e12..    x10 + 3*x11 + x12 - x13 + x14 =E= 1;

e13..    2*x11 - 3*x12 =E= 0;

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;