MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance ex9_2_7

Formatsⓘ	ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)ⓘ	17.00000000 p1 ( gdx sol ) (infeas: 4e-16)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	16.99999998 (ANTIGONE) 16.99999998 (BARON) 17.00000000 (COUENNE) 17.00000000 (GUROBI) 17.00000000 (LINDO) 17.00000000 (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. Visweswaran, V, Floudas, C A, Ierapetritou, M G, and Pistikopoulos, E N, A Decomposition-Based Global Optimization Approach for Solving Bilevel Linear and Quadratic Programs. Chapter 10 in Floudas, C A and Pardalos, P M, Eds, State of the Art in Global Optimization, Kluwer Academic Publishers, 1996, 139-162.
Sourceⓘ	Test Problem ex9.2.7 of Chapter 9 of Floudas e.a. handbook
Added to libraryⓘ	31 Jul 2001
Problem typeⓘ	QCQP
#Variablesⓘ	10
#Binary Variablesⓘ	0
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	10
#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ⓘ	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ⓘ	25
#Nonlinear Nonzeros in Jacobianⓘ	8
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	10
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	2
#Blocks in Hessian of Lagrangianⓘ	6
Minimal blocksize in Hessian of Lagrangianⓘ	1
Maximal blocksize in Hessian of Lagrangianⓘ	2
Average blocksize in Hessian of Lagrangianⓘ	1.666667
#Semicontinuitiesⓘ	0
#Nonlinear Semicontinuitiesⓘ	0
#SOS type 1ⓘ	0
#SOS type 2ⓘ	0
Minimal coefficientⓘ	5.0000e-01
Maximal coefficientⓘ	5.0000e+00
Infeasibility of initial pointⓘ	7
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
*         28       18       10        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.. (-5 + x2)*(-5 + x2) + (1 + 2*x3)*(1 + 2*x3) - objvar =E= 0;

e2..  - 3*x2 + x3 + x4 =E= -3;

e3..    x2 - 0.5*x3 + x5 =E= 4;

e4..    x2 + x3 + x6 =E= 7;

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

e6.. x4*x8 =E= 0;

e7.. x5*x9 =E= 0;

e8.. x6*x10 =E= 0;

e9.. x7*x11 =E= 0;

e10..  - 1.5*x2 + 2*x3 + x8 - 0.5*x9 + x10 - x11 =E= 2;

* set non-default bounds
x4.up = 20;
x5.up = 20;
x6.up = 20;
x7.up = 20;
x8.up = 20;
x9.up = 20;
x10.up = 20;
x11.up = 20;

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;