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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance: ex5_2_4

Formats ams gms lp mod nl osil pip
Primal Bounds
-0.00000000 p1 ( gdx sol )
(infeas: 0)
-450.00000000 p2 ( gdx sol )
(infeas: 3e-14)
Dual Bounds
-450.00000050 (ANTIGONE)
-450.00000090 (BARON)
-450.00026250 (COUENNE)
-450.00000000 (LINDO)
-450.00000080 (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.
Ben-Tal, A, Eiger, G, and Gershovitz, V, Global Minimization by Reducing the Duality Gap, Mathematical Programming, 63:1, 1994, 193-212.
Source Test Problem ex5.2.4 of Chapter 5 of Floudas e.a. handbook
Added to library 31 Jul 2001
Problem type QCQP
#Variables 7
#Binary Variables 0
#Integer Variables 0
#Nonlinear Variables 5
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense min
Objective type quadratic
Objective curvature indefinite
#Nonzeros in Objective 7
#Nonlinear Nonzeros in Objective 5
#Constraints 6
#Linear Constraints 3
#Quadratic Constraints 3
#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 11
#Nonzeros in (Upper-Left) Hessian of Lagrangian 12
#Nonzeros in Diagonal of Hessian of Lagrangian 0
#Blocks in Hessian of Lagrangian 1
Minimal blocksize in Hessian of Lagrangian 5
Maximal blocksize in Hessian of Lagrangian 5
Average blocksize in Hessian of Lagrangian 5.0
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Infeasibility of initial point 1
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
*          7        2        0        5        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*          8        8        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         28       12       16        0
*
*  Solve m using NLP minimizing objvar;


Variables  x1,x2,x3,x4,x5,x6,x7,objvar;

Positive Variables  x1,x2,x3,x4,x5,x6,x7;

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


e1.. -((9 - 6*x1 - 16*x2 - 15*x3)*x4 + (15 - 6*x1 - 16*x2 - 15*x3)*x5) + x6
      - 5*x7 - objvar =E= 0;

e2.. x3*x4 + x3*x5 =L= 50;

e3..    x4 + x6 =L= 100;

e4..    x5 + x7 =L= 200;

e5.. (-2.5 + 3*x1 + x2 + x3)*x4 - 0.5*x6 =L= 0;

e6.. (-1.5 + 3*x1 + x2 + x3)*x5 + 0.5*x7 =L= 0;

e7..    x1 + x2 + x3 =E= 1;

* set non-default bounds
x1.up = 1;
x2.up = 1;
x3.up = 1;
x4.up = 100;
x5.up = 200;
x6.up = 100;
x7.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: 2018-12-11 Git hash: 9abab1ba
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