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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
Primal Bounds
-13.00000000 p1 ( gdx sol )
(infeas: 0)
Dual Bounds
-13.00000001 (ANTIGONE)
-13.00000000 (BARON)
-13.00000000 (COUENNE)
-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
Infeasibility of initial point 48
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
*         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;


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