MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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


Instance st_e27

Formats ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)
2.00000000 p1 ( gdx sol )
(infeas: 0)
Other points (infeas > 1e-08)  
Dual Bounds
2.00000000 (ANTIGONE)
2.00000000 (BARON)
2.00000000 (COUENNE)
2.00000000 (CPLEX)
2.00000000 (GUROBI)
2.00000000 (LINDO)
2.00000000 (SCIP)
2.00000000 (SHOT)
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 Soland, R M, An algorithm for separable nonconvex programming problems, Management Science, 15:9, 1969, 550-569.
Source BARON book instance misc/e27
Added to library 01 Sep 2002
Problem type MBQP
#Variables 4
#Binary Variables 2
#Integer Variables 0
#Nonlinear Variables 2
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense min
Objective type quadratic
Objective curvature concave
#Nonzeros in Objective 4
#Nonlinear Nonzeros in Objective 2
#Constraints 6
#Linear Constraints 6
#Quadratic Constraints 0
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature linear
#Nonzeros in Jacobian 12
#Nonlinear Nonzeros in Jacobian 0
#Nonzeros in (Upper-Left) Hessian of Lagrangian 2
#Nonzeros in Diagonal of Hessian of Lagrangian 2
#Blocks in Hessian of Lagrangian 2
Minimal blocksize in Hessian of Lagrangian 1
Maximal blocksize in Hessian of Lagrangian 1
Average blocksize in Hessian of Lagrangian 1.0
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Minimal coefficient 1.0000e+00
Maximal coefficient 6.0000e+00
Infeasibility of initial point 0
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        1        0        6        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*          5        3        2        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         17       15        2        0
*
*  Solve m using MINLP minimizing objvar;


Variables  b1,b2,x3,x4,objvar;

Positive Variables  x3,x4;

Binary Variables  b1,b2;

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


e1..  - x3 + 3*x4 =L= 5;

e2..    2*x3 - x4 =L= 5;

e3..  - 2*x3 + x4 =L= 0;

e4..    x3 - 3*x4 =L= 0;

e5..  - 6*b1 + x3 =L= 0;

e6..  - 5*b2 + x4 =L= 0;

e7.. -(4*x3 - sqr(x3) - sqr(x4) + 2*x4) - 2*b1 - 2*b2 + objvar =E= 2;

* set non-default bounds
x3.up = 6;
x4.up = 5;

Model m / all /;

m.limrow=0; m.limcol=0;
m.tolproj=0.0;

$if NOT '%gams.u1%' == '' $include '%gams.u1%'

$if not set MINLP $set MINLP MINLP
Solve m using %MINLP% minimizing objvar;


Last updated: 2022-05-24 Git hash: 1198c186
Imprint / Privacy Policy / License: CC-BY 4.0