MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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


Instance nvs19

Formats ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)
-1098.40000000 p1 ( gdx sol )
(infeas: 0)
Other points (infeas > 1e-08)  
Dual Bounds
-1098.40000000 (ANTIGONE)
-1098.40000000 (BARON)
-1098.40000000 (COUENNE)
-1098.40000000 (GUROBI)
-1098.40000000 (LINDO)
-1098.40000000 (SCIP)
-1098.60000000 (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/gupta19
Added to library 25 Jul 2002
Problem type IQCQP
#Variables 8
#Binary Variables 0
#Integer Variables 8
#Nonlinear Variables 8
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 8
Objective Sense min
Objective type quadratic
Objective curvature convex
#Nonzeros in Objective 8
#Nonlinear Nonzeros in Objective 8
#Constraints 8
#Linear Constraints 0
#Quadratic Constraints 8
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature indefinite
#Nonzeros in Jacobian 64
#Nonlinear Nonzeros in Jacobian 64
#Nonzeros in (Upper-Left) Hessian of Lagrangian 64
#Nonzeros in Diagonal of Hessian of Lagrangian 8
#Blocks in Hessian of Lagrangian 1
Minimal blocksize in Hessian of Lagrangian 8
Maximal blocksize in Hessian of Lagrangian 8
Average blocksize in Hessian of Lagrangian 8.0
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Minimal coefficient 2.0000e+00
Maximal coefficient 1.2680e+02
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
*          9        1        8        0        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*          9        1        0        8        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         73        1       72        0
*
*  Solve m using MINLP minimizing objvar;


Variables  i1,i2,i3,i4,i5,i6,i7,i8,objvar;

Integer Variables  i1,i2,i3,i4,i5,i6,i7,i8;

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


e1.. (-9*sqr(i1)) - 10*i1*i2 - 8*sqr(i2) - 5*sqr(i3) - 6*i3*i1 - 10*i3*i2 - 7*
     sqr(i4) - 10*i4*i1 - 6*i4*i2 - 2*i4*i3 - 2*i5*i2 - 7*sqr(i5) - 6*i6*i1 - 2
     *i6*i2 - 2*i6*i4 - 5*sqr(i6) + 6*i7*i1 + 2*i7*i2 + 4*i7*i3 + 2*i7*i4 - 4*
     i7*i5 + 4*i7*i6 - 8*sqr(i7) - 2*i8*i1 - 8*i8*i2 - 2*i8*i3 + 6*i8*i5 - 2*i8
     *i7 - 6*sqr(i8) =G= -1980;

e2.. (-6*sqr(i1)) - 8*i1*i2 - 6*sqr(i2) - 4*sqr(i3) - 2*i3*i1 - 2*i3*i2 - 8*
     sqr(i4) + 2*i4*i1 + 10*i4*i2 - 2*i5*i1 - 6*i5*i2 + 6*i5*i4 + 7*sqr(i5) - 2
     *i6*i2 + 8*i6*i3 + 2*i6*i4 - 4*i6*i5 - 8*sqr(i6) - 6*i7*i1 - 10*i7*i2 - 2*
     i7*i3 + 10*i7*i4 - 10*i7*i5 - 8*sqr(i7) - 2*i8*i1 - 4*i8*i2 - 2*i8*i3 - 8*
     i8*i5 - 8*i8*i7 - 5*sqr(i8) =G= -3180;

e3.. (-9*sqr(i1)) - 6*sqr(i2) - 8*sqr(i3) + 2*i2*i1 + 2*i3*i2 - 6*sqr(i4) + 4*
     i4*i1 + 4*i4*i2 - 2*i4*i3 - 6*i5*i1 - 2*i5*i2 + 4*i5*i4 + 6*sqr(i5) + 2*i6
     *i1 + 4*i6*i2 - 6*i6*i4 - 2*i6*i5 - 5*sqr(i6) + 2*i7*i2 - 4*i7*i3 - 6*i7*
     i5 - 4*i7*i6 - 7*sqr(i7) - 2*i8*i1 + 4*i8*i3 + 2*i8*i4 - 4*sqr(i8)
      =G= -1830;

e4.. (-8*sqr(i1)) - 4*sqr(i2) - 9*sqr(i3) - 7*sqr(i4) - 2*i2*i1 - 2*i3*i1 - 4*
     i3*i2 + 6*i4*i1 + 2*i4*i2 - 2*i4*i3 - 6*i5*i1 - 4*i5*i2 - 2*i5*i3 + 6*i5*
     i4 + 6*sqr(i5) - 10*i6*i1 - 10*i6*i3 + 4*i6*i4 - 2*i6*i5 - 7*sqr(i6) + 6*
     i7*i1 - 2*i7*i2 - 2*i7*i3 + 6*i7*i5 + 2*i7*i6 - 6*sqr(i7) + 4*i8*i1 - 4*i8
     *i2 + 2*i8*i3 - 4*i8*i4 - 4*i8*i5 + 8*i8*i6 + 6*i8*i7 - 8*sqr(i8)
      =G= -1610;

e5.. 2*i2*i1 - 4*sqr(i1) - 5*sqr(i2) - 6*i3*i1 - 8*sqr(i3) - 2*i4*i1 + 6*i4*i2
      - 2*i4*i3 - 6*sqr(i4) - 4*i5*i1 + 2*i5*i2 - 6*i5*i3 - 8*i5*i4 - 7*sqr(i5)
      + 4*i6*i1 - 4*i6*i2 + 6*i6*i3 + 4*i6*i5 - 7*sqr(i6) + 4*i7*i1 - 4*i7*i2
      - 4*i7*i3 + 4*i7*i4 + 4*i7*i5 + 4*i7*i6 - 8*sqr(i7) - 2*i8*i1 + 4*i8*i4
      + 2*i8*i6 + 2*i8*i7 - 4*sqr(i8) =G= -1180;

e6.. 2*i2*i1 - 7*sqr(i1) - 7*sqr(i2) - 6*i3*i1 - 2*i3*i2 - 6*sqr(i3) - 2*i4*i1
      + 2*i4*i2 - 2*i4*i3 - 5*sqr(i4) - 2*i5*i1 - 4*i5*i3 + 2*i5*i4 - 5*sqr(i5)
      + 2*i6*i1 - 4*i6*i2 + 4*i6*i3 + 2*i6*i4 + 6*i6*i5 - 9*sqr(i6) + 4*i7*i2
      - 4*i7*i3 + 4*i7*i4 - 4*i7*i5 + 8*i7*i6 - 6*sqr(i7) + 4*i8*i1 + 8*i8*i2
      + 2*i8*i3 - 4*i8*i4 - 2*i8*i5 + 4*i8*i6 - 9*sqr(i8) =G= -930;

e7.. (-9*sqr(i1)) - 4*i2*i1 - 8*sqr(i2) + 4*i3*i1 + 2*i3*i2 - 7*sqr(i3) + 4*i4*
     i1 + 4*i4*i3 - 7*sqr(i4) - 2*i5*i1 - 12*i5*i2 - 4*i5*i3 - 8*sqr(i5) - 8*i6
     *i1 + 2*i6*i2 - 2*i6*i5 - 6*sqr(i6) - 4*i7*i1 - 6*i7*i2 - 2*i7*i3 + 10*i7*
     i4 - 2*i7*i5 + 2*i7*i6 - 7*sqr(i7) - 2*i8*i1 + 2*i8*i2 + 2*i8*i3 + 2*i8*i4
      - 6*i8*i6 - 2*i8*i7 - 6*sqr(i8) =G= -2790;

e8.. 4*i2*i1 - 7*sqr(i1) - 8*sqr(i2) + 4*i3*i1 - 8*sqr(i3) + 4*i4*i1 + 8*i4*i2
      - 6*i4*i3 - 7*sqr(i4) - 2*i5*i2 + 2*i5*i4 - 5*sqr(i5) - 2*i6*i1 - 2*i6*i2
      + 4*i6*i4 - 4*i6*i5 - 7*sqr(i6) - 2*i7*i1 + 8*i7*i2 - 2*i7*i3 - 2*i7*i4
      + 6*i7*i5 + 2*i7*i6 - 7*sqr(i7) + 2*i8*i1 - 6*i8*i2 + 6*i8*i3 + 4*i8*i4
      + 2*i8*i5 - 4*i8*i6 - 6*sqr(i8) =G= -910;

e9.. -(7*sqr(i1) + 6*sqr(i2) + 20.2*i1 - 8.6*i2 + 8*sqr(i3) - 6*i3*i1 + 4*i3*i2
      + 9.4*i3 + 6*sqr(i4) + 2*i4*i1 + 2*i4*i3 - 30.8*i4 + 7*sqr(i5) - 4*i5*i1
      - 2*i5*i2 - 6*i5*i3 - 126.8*i5 + 4*sqr(i6) + 2*i6*i1 - 4*i6*i2 - 4*i6*i3
      - 2*i6*i4 + 6*i6*i5 - 81.4*i6 + 6*sqr(i7) - 2*i7*i1 - 6*i7*i2 - 2*i7*i3
      + 4*i7*i5 + 4*i7*i6 - 94*i7 + 7*sqr(i8) - 4*i8*i1 - 2*i8*i2 + 6*i8*i3 + 4
     *i8*i4 - 4*i8*i5 - 2*i8*i6 + 4*i8*i7 - 9.4*i8) + objvar =E= 0;

* set non-default bounds
i1.up = 200;
i2.up = 200;
i3.up = 200;
i4.up = 200;
i5.up = 200;
i6.up = 200;
i7.up = 200;
i8.up = 200;

* set non-default levels
i1.l = 1;
i2.l = 1;
i3.l = 1;
i4.l = 1;
i5.l = 1;
i6.l = 1;
i7.l = 1;
i8.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: 2022-05-24 Git hash: 1198c186
Imprint / Privacy Policy / License: CC-BY 4.0