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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance: ex9_2_6

Formats ams gms lp mod nl osil pip
Primal Bounds
-1.00000000 p1 ( gdx sol )
(infeas: 0)
Dual Bounds
-1.00000001 (ANTIGONE)
-1.00000000 (BARON)
-1.00000000 (COUENNE)
-1.00000000 (LINDO)
-1.00000000 (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.
Falk, J E and Liu, J, On Bilevel Programming, Part I: General Nonlinear Cases, Mathematical Programming, 70:1-3, 1995, 47-72.
Source Test Problem ex9.2.6 of Chapter 9 of Floudas e.a. handbook
Added to library 31 Jul 2001
Problem type QCQP
#Variables 16
#Binary Variables 0
#Integer Variables 0
#Nonlinear Variables 16
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense min
Objective type quadratic
Objective curvature convex
#Nonzeros in Objective 4
#Nonlinear Nonzeros in Objective 4
#Constraints 12
#Linear Constraints 6
#Quadratic Constraints 6
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature indefinite
#Nonzeros in Jacobian 28
#Nonlinear Nonzeros in Jacobian 12
#Nonzeros in (Upper-Left) Hessian of Lagrangian 16
#Nonzeros in Diagonal of Hessian of Lagrangian 4
#Blocks in Hessian of Lagrangian 10
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
Infeasibility of initial point 1.5
Sparsity Jacobian Sparsity of Objective Gradient and Jacobian
Sparsity Hessian of Lagrangian Sparsity of 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
*         17       17        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         33       17       16        0
*
*  Solve m using NLP minimizing objvar;


Variables  objvar,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17;

Positive Variables  x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17;

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


e1.. x2*x2 - 2*x2 + x3*x3 - 2*x3 + x4*x4 + x5*x5 - objvar =E= 0;

e2..  - x4 + x6 =E= -0.5;

e3..  - x5 + x7 =E= -0.5;

e4..    x4 + x8 =E= 1.5;

e5..    x5 + x9 =E= 1.5;

e6.. x6*x12 =E= 0;

e7.. x7*x13 =E= 0;

e8.. x8*x14 =E= 0;

e9.. x9*x15 =E= 0;

e10.. x10*x16 =E= 0;

e11.. x11*x17 =E= 0;

e12..  - 2*x2 + 2*x4 - x12 + x14 =E= 0;

e13..  - 2*x3 + 2*x5 - x13 + x15 =E= 0;

* set non-default bounds
x6.up = 200;
x7.up = 200;
x8.up = 200;
x9.up = 200;
x10.up = 200;
x11.up = 200;
x12.up = 200;
x13.up = 200;
x14.up = 200;
x15.up = 200;
x16.up = 200;
x17.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;


Last updated: 2018-09-14 Git hash: ac5a5314
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