MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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


Instance synthes1

Formats ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)
6.00975909 p1 ( gdx sol )
(infeas: 0)
Other points (infeas > 1e-08)  
Dual Bounds
6.00975891 (ALPHAECP)
6.00975909 (ANTIGONE)
6.00975909 (BARON)
6.00975891 (BONMIN)
6.00975909 (COUENNE)
6.00975909 (LINDO)
6.00975909 (SCIP)
6.00974224 (SHOT)
References Duran, Marco A and Grossmann, I E, An Outer-Approximation Algorithm for a Class of Mixed-integer Nonlinear Programs, Mathematical Programming, 36:3, 1986, 307-339.
Source MacMINLP model synthes1.mod
Application Synthesis of processing system
Added to library 01 May 2001
Problem type MBNLP
#Variables 6
#Binary Variables 3
#Integer Variables 0
#Nonlinear Variables 2
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense min
Objective type nonlinear
Objective curvature convex
#Nonzeros in Objective 6
#Nonlinear Nonzeros in Objective 2
#Constraints 6
#Linear Constraints 4
#Quadratic Constraints 0
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 2
Operands in Gen. Nonlin. Functions log
Constraints curvature convex
#Nonzeros in Jacobian 16
#Nonlinear Nonzeros in Jacobian 4
#Nonzeros in (Upper-Left) Hessian of Lagrangian 4
#Nonzeros in Diagonal of Hessian of Lagrangian 2
#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 8.0000e-01
Maximal coefficient 1.9200e+01
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        2        4        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*          7        4        3        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         23       17        6        0
*
*  Solve m using MINLP minimizing objvar;


Variables  x1,x2,x3,b4,b5,b6,objvar;

Positive Variables  x1,x2,x3;

Binary Variables  b4,b5,b6;

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


e1.. -(-18*log(1 + x2) - 19.2*log(1 + x1 - x2) + 10*x1) + 7*x3 - 5*b4 - 6*b5
      - 8*b6 + objvar =E= 10;

e2.. 0.8*log(1 + x2) + 0.96*log(1 + x1 - x2) - 0.8*x3 =G= 0;

e3.. log(1 + x2) + 1.2*log(1 + x1 - x2) - x3 - 2*b6 =G= -2;

e4..  - x1 + x2 =L= 0;

e5..    x2 - 2*b4 =L= 0;

e6..    x1 - x2 - 2*b5 =L= 0;

e7..    b4 + b5 =L= 1;

* set non-default bounds
x1.up = 2;
x2.up = 2;
x3.up = 1;

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: 2022-08-11 Git hash: f176bd52
Imprint / Privacy Policy / License: CC-BY 4.0