MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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


Instance st_glmp_fp2

Formats ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)
7.62750000 p1 ( gdx sol )
(infeas: 0)
7.34454542 p2 ( gdx sol )
(infeas: 6e-10)
Other points (infeas > 1e-08)  
Dual Bounds
7.34454541 (ANTIGONE)
7.34454541 (BARON)
7.34454542 (COUENNE)
7.34454542 (CPLEX)
7.34454540 (GUROBI)
7.34454542 (LINDO)
7.34454542 (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.
Falk, J E and Polocsay, S W, Image space analysis of generalized fractional programs, Journal of Global Optimization, 4:1, 1994, 63-88.
Added to library 03 Sep 2002
Problem type QP
#Variables 4
#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 2
#Nonlinear Nonzeros in Objective 2
#Constraints 9
#Linear Constraints 9
#Quadratic Constraints 0
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature linear
#Nonzeros in Jacobian 20
#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 2.0000e+00
Infeasibility of initial point 7
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
*         10        3        2        5        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*          5        5        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         23       21        2        0
*
*  Solve m using NLP minimizing objvar;


Variables  x1,x2,x3,x4,objvar;

Positive Variables  x1,x2;

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


e1..    2*x1 + x2 =L= 14;

e2..    x1 + x2 =L= 10;

e3..    1.44*x1 + x2 =G= 4.89;

e4..  - 1.58*x1 + x2 =L= 5.65;

e5..  - 1.03*x1 + x2 =L= 5.93;

e6..    x1 + 2*x2 =G= 6;

e7..    x1 - x2 =L= 3;

e8.. -x3*x4 + objvar =E= 0;

e9..    x1 + x2 - x3 =E= 0;

e10..    x1 - x2 - x4 =E= -7;

* set non-default bounds
x1.up = 5;
x2.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: 2022-08-11 Git hash: f176bd52
Imprint / Privacy Policy / License: CC-BY 4.0