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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance: ex7_3_3

Formats ams gms lp mod nl osil pip
Primal Bounds
1.14477980 p1 ( gdx sol )
(infeas: 2e-15)
0.81752905 p2 ( gdx sol )
(infeas: 1e-14)
Dual Bounds
0.81752904 (ANTIGONE)
0.81752904 (BARON)
0.81752905 (COUENNE)
0.81752905 (LINDO)
0.81752889 (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.
Ackermann, J, Kaesbauer, D, and Muench, R, Robust Gamma-Stability Analysis in a Plant Parameter Space, Automatica, 27:1, 1991, 75-85.
Source Test Problem ex7.3.3 of Chapter 7 of Floudas e.a. handbook
Added to library 31 Jul 2001
Problem type QCP
#Variables 5
#Binary Variables 0
#Integer Variables 0
#Nonlinear Variables 3
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense min
Objective type linear
Objective curvature linear
#Nonzeros in Objective 1
#Nonlinear Nonzeros in Objective 0
#Constraints 8
#Linear Constraints 6
#Quadratic Constraints 2
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature indefinite
#Nonzeros in Jacobian 20
#Nonlinear Nonzeros in Jacobian 5
#Nonzeros in (Upper-Left) Hessian of Lagrangian 5
#Nonzeros in Diagonal of Hessian of Lagrangian 1
#Blocks in Hessian of Lagrangian 1
Minimal blocksize in Hessian of Lagrangian 3
Maximal blocksize in Hessian of Lagrangian 3
Average blocksize in Hessian of Lagrangian 3.0
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Infeasibility of initial point 44
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
*          9        3        0        6        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*          6        6        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         22       17        5        0
*
*  Solve m using NLP minimizing objvar;


Variables  x1,x2,x3,x4,x5,objvar;

Positive Variables  x4;

Equations  e1,e2,e3,e4,e5,e6,e7,e8,e9;


e1..  - x5 + objvar =E= 0;

e2.. 9.625*x1*x4 - 4*x1 - 78*x4 + 16*x2*x4 - x2 + 16*sqr(x4) + x3 =E= -12;

e3.. 16*x1*x4 - 19*x1 - 24*x4 - 8*x2 - x3 =E= -44;

e4..    x1 - 0.25*x5 =L= 2.25;

e5..  - x1 - 0.25*x5 =L= -2.25;

e6..  - x2 - 0.5*x5 =L= -1.5;

e7..    x2 - 0.5*x5 =L= 1.5;

e8..  - x3 - 1.5*x5 =L= -1.5;

e9..    x3 - 1.5*x5 =L= 1.5;

* set non-default bounds
x4.up = 10;

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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