MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

Home // Instances // Documentation // Download // Statistics


Instance st_glmp_ss1

Formats ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)
-24.57142857 p1 ( gdx sol )
(infeas: 2e-15)
Other points (infeas > 1e-08)  
Dual Bounds
-24.57142860 (ANTIGONE)
-24.57142860 (BARON)
-24.57142858 (COUENNE)
-24.57142857 (CPLEX)
-24.57143490 (GUROBI)
-24.57142893 (LINDO)
-24.57142857 (SCIP)
References Tawarmalani, M and Sahinidis, N V, Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming: Theory, Algorithms, Software, and Applications, Kluwer, 2002.
Schaible, S and Sodini, C, Finite algorithm for generalized linear multiplicative programming, Journal of Optimization Theory and Applications, 87:2, 1995, 441-455.
Added to library 03 Sep 2002
Problem type QP
#Variables 5
#Binary Variables 0
#Integer Variables 0
#Nonlinear Variables 2
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense min
Objective type quadratic
Objective curvature indefinite
#Nonzeros in Objective 3
#Nonlinear Nonzeros in Objective 2
#Constraints 11
#Linear Constraints 11
#Quadratic Constraints 0
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature linear
#Nonzeros in Jacobian 24
#Nonlinear Nonzeros in Jacobian 0
#Nonzeros in (Upper-Left) Hessian of Lagrangian 2
#Nonzeros in Diagonal of Hessian of Lagrangian 0
#Blocks in Hessian of Lagrangian 1
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
Minimal coefficient 1.0000e+00
Maximal coefficient 4.0000e+00
Infeasibility of initial point 12
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
*         12        4        0        8        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
*         28       26        2        0
*
*  Solve m using NLP minimizing objvar;


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

Positive Variables  x1,x2;

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


e1..    x1 - 2*x2 =L= 100;

e2..  - 3*x1 - 4*x2 =L= -12;

e3..  - x1 - x2 =L= 100;

e4..  - x1 + 4*x2 =L= 100;

e5..  - x1 + 2*x2 =L= 18;

e6..    3*x1 + 4*x2 =L= 100;

e7..    x1 + x2 =L= 13;

e8..    x1 - 4*x2 =L= 8;

e9..    x1 - x4 =E= 0;

e10..    x1 - x2 - x5 =E= -10;

e11..    x1 + x2 - x6 =E= 6;

e12.. -x5*x6 + objvar - x4 =E= 0;

* set non-default bounds
x1.up = 13;
x2.up = 13;

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: 2022-10-14 Git hash: 2be6d7c0
Imprint / Privacy Policy / License: CC-BY 4.0