MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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


Instance nvs22

Formats ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)
6.05822000 p1 ( gdx sol )
(infeas: 2e-12)
Other points (infeas > 1e-08)  
Dual Bounds
6.05822000 (ANTIGONE)
6.05822000 (BARON)
6.05822000 (COUENNE)
6.05822000 (LINDO)
6.05822000 (SCIP)
1.82636000 (SHOT)
References Gupta, Omprakash K and Ravindran, A, Branch and Bound Experiments in Convex Nonlinear Integer Programming, Management Science, 13:12, 1985, 1533-1546.
Tawarmalani, M and Sahinidis, N V, Exact Algorithms for Global Optimization of Mixed-Integer Nonlinear Programs. In Pardalos, Panos M and Romeijn, H Edwin, Eds, Handbook of Global Optimization - Volume 2: Heuristic Approaches, Kluwer Academic Publishers, 65-85.
Tawarmalani, M and Sahinidis, N V, Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming: Theory, Algorithms, Software, and Applications, Kluwer, 2002.
Source BARON book instance gupta/gupta22
Added to library 25 Jul 2002
Problem type MINLP
#Variables 8
#Binary Variables 0
#Integer Variables 4
#Nonlinear Variables 8
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 4
Objective Sense min
Objective type polynomial
Objective curvature indefinite
#Nonzeros in Objective 4
#Nonlinear Nonzeros in Objective 4
#Constraints 9
#Linear Constraints 1
#Quadratic Constraints 0
#Polynomial Constraints 0
#Signomial Constraints 4
#General Nonlinear Constraints 4
Operands in Gen. Nonlin. Functions div mul power sqr sqrt
Constraints curvature indefinite
#Nonzeros in Jacobian 26
#Nonlinear Nonzeros in Jacobian 20
#Nonzeros in (Upper-Left) Hessian of Lagrangian 30
#Nonzeros in Diagonal of Hessian of Lagrangian 8
#Blocks in Hessian of Lagrangian 2
Minimal blocksize in Hessian of Lagrangian 3
Maximal blocksize in Hessian of Lagrangian 5
Average blocksize in Hessian of Lagrangian 4.0
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Minimal coefficient 2.0474e-02
Maximal coefficient 1.0000e+13
Infeasibility of initial point 3.3e+04
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        5        5        0        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*          9        5        0        4        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         31        7       24        0
*
*  Solve m using MINLP minimizing objvar;


Variables  i1,i2,i3,i4,x5,x6,x7,x8,objvar;

Integer Variables  i1,i2,i3,i4;

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


e1.. -4243.28147100424/(i3*i4) + x5 =E= 0;

e2.. -sqrt(0.25*sqr(i4) + sqr(0.5*i1 + 0.5*i3)) + x7 =E= 0;

e3.. -(59405.9405940594 + 2121.64073550212*i4)*x7/(i3*i4*(0.0833333333333333*
     sqr(i4) + sqr(0.5*i1 + 0.5*i3))) + x6 =E= 0;

e4.. -0.5*i4/x7 + x8 =E= 0;

e5.. -sqrt(sqr(x5) + 2*x5*x6*x8 + sqr(x6)) =G= -13600;

e6.. -504000/(sqr(i1)*i2) =G= -30000;

e7..    i2 - i3 =G= 0;

e8.. 0.0204744897959184*sqrt(10000000000000*POWER(i2,3)*i1*i1*POWER(i2,3))*(1
      - 0.0282346219657891*i1) =G= 6000;

e9.. -2.1952/(POWER(i1,3)*i2) =G= -0.25;

e10.. -(1.10471*i3**2*i4 + 0.04811*i1*i2*(14 + i4)) + objvar =E= 0;

* set non-default bounds
i1.lo = 1; i1.up = 200;
i2.lo = 1; i2.up = 200;
i3.lo = 1; i3.up = 20;
i4.lo = 1; i4.up = 20;

* set non-default levels
i1.l = 2;
i2.l = 2;
i3.l = 2;
i4.l = 2;
x5.l = 1;
x6.l = 1;
x7.l = 1;
x8.l = 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: 2022-04-26 Git hash: de668763
Imprint / Privacy Policy / License: CC-BY 4.0