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Instance nvs24

Formats ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)
-1033.20000000 p1 ( gdx sol )
(infeas: 0)
Other points (infeas > 1e-08)  
Dual Bounds
-1033.20000100 (ANTIGONE)
-1033.20000000 (BARON)
-1033.20000000 (COUENNE)
-1033.20000000 (GUROBI)
-4887.06785500 (LINDO)
-1033.20000000 (SCIP)
-1033.20000000 (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/gupta24
Added to library 25 Jul 2002
Problem type IQCQP
#Variables 10
#Binary Variables 0
#Integer Variables 10
#Nonlinear Variables 10
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 10
Objective Sense min
Objective type quadratic
Objective curvature convex
#Nonzeros in Objective 10
#Nonlinear Nonzeros in Objective 10
#Constraints 10
#Linear Constraints 0
#Quadratic Constraints 10
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature indefinite
#Nonzeros in Jacobian 100
#Nonlinear Nonzeros in Jacobian 100
#Nonzeros in (Upper-Left) Hessian of Lagrangian 100
#Nonzeros in Diagonal of Hessian of Lagrangian 10
#Blocks in Hessian of Lagrangian 1
Minimal blocksize in Hessian of Lagrangian 10
Maximal blocksize in Hessian of Lagrangian 10
Average blocksize in Hessian of Lagrangian 10.0
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Minimal coefficient 2.0000e+00
Maximal coefficient 1.2500e+02
Infeasibility of initial point 1.188e+06
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
*         11        1       10        0        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         11        1        0       10        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        111        1      110        0
*
*  Solve m using MINLP minimizing objvar;


Variables  i1,i2,i3,i4,i5,i6,i7,i8,i9,i10,objvar;

Integer Variables  i1,i2,i3,i4,i5,i6,i7,i8,i9,i10;

Equations  e1,e2,e3,e4,e5,e6,e7,e8,e9,e10,e11;


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 - 6*i8*i2 - 2*i8*i3 + 6*i8*i5 - 2*i8
     *i7 - 6*sqr(i8) + 2*i9*i3 - 4*i9*i4 + 8*i9*i5 + 4*i9*i6 - 6*i9*i8 - 6*sqr(
     i9) + 2*i10*i1 + 2*i10*i2 - 2*i10*i4 + 2*i10*i5 - 2*i10*i6 - 2*i10*i8 - 6*
     i10*i9 - 8*sqr(i10) =G= -1930;

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) - 2*i9*i1 - 2*i9*i2 + 4*i9*i6 + 2*i9*i7 - 6*
     sqr(i9) + 4*i10*i1 - 2*i10*i3 + 4*i10*i4 + 6*i10*i6 - 2*i10*i7 - 2*i10*i8
      - 6*sqr(i10) =G= -3140;

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) + 10*i9
     *i1 + 6*i9*i2 - 4*i9*i3 - 10*i9*i4 + 8*i9*i5 - 6*i9*i6 - 2*i9*i7 - 8*sqr(
     i9) - 4*i10*i2 + 2*i10*i3 + 4*i10*i4 + 6*i10*i5 + 2*i10*i7 - 2*i10*i8 + 2*
     i10*i9 - 7*sqr(i10) + 4*i10*i6 =G= -1600;

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*i6 - 8*sqr(i8) - 4*i9*
     i1 + 4*i9*i2 + 6*i9*i3 - 2*i9*i4 + 2*i9*i6 + 8*i9*i7 - 4*i9*i8 - 10*sqr(i9
     ) + 8*i10*i1 + 4*i10*i2 + 2*i10*i3 + 2*i10*i4 + 4*i10*i6 - 6*sqr(i10)
      =G= -1260;

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) - 2*i9*i2 + 4*i9*i3 + 4*i9*i4 - 2*i9*i5
      + 2*i9*i6 + 6*i9*i7 - 6*i9*i8 - 7*sqr(i9) - 6*i10*i3 - 2*i10*i4 - 4*i10*
     i5 - 4*i10*i9 - 8*sqr(i10) + 2*i10*i8 =G= -1430;

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) - 4*i9*i1 + 2*i9*i4
      + 6*i9*i5 - 4*i9*i6 - 2*i9*i7 + 2*i9*i8 - 6*sqr(i9) + 2*i10*i1 - 2*i10*i5
      - 4*i10*i6 + 2*i10*i7 + 2*i10*i8 + 6*i10*i9 - 5*sqr(i10) =G= -1020;

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) + 4*i9*i1 + 2*i9*i2 + 4*i9*i3 + 4*i9*i4
      + 2*i9*i5 - 2*i9*i6 - 9*sqr(i9) + 6*i10*i1 - 6*i10*i3 + 10*i10*i4 + 6*i10
     *i6 - 8*i10*i7 - 4*i10*i9 - 8*sqr(i10) =G= -2860;

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) + 4*i9*i1 - 6*i9*i2 + 2*i9*i3 - 2*i9*i4
      + 2*i9*i5 + 6*i9*i6 + 2*i9*i7 - 4*i9*i8 - 6*sqr(i9) - 2*i10*i1 - 2*i10*i2
      - 4*i10*i3 + 4*i10*i5 + 4*i10*i6 + 2*i10*i8 - 4*i10*i9 - 6*sqr(i10)
      =G= -880;

e9.. 2*i2*i1 - 4*sqr(i1) - 7*sqr(i2) + 8*i3*i1 - 4*i3*i2 - 9*sqr(i3) - 2*i4*i1
      - 4*i4*i2 - 2*i4*i3 - 6*sqr(i4) + 4*i5*i1 + 2*i5*i2 + 4*i5*i3 + 6*i5*i4
      - 6*sqr(i5) + 4*i6*i3 - 6*i6*i4 - 7*sqr(i6) - 2*i7*i2 - 4*i7*i3 + 4*i7*i5
      + 8*i7*i6 - 7*sqr(i7) + 2*i8*i2 - 4*i8*i3 + 2*i8*i4 + 2*i8*i5 + 6*i8*i7
      - 7*sqr(i8) + 4*i9*i1 + 2*i9*i2 - 10*i9*i3 + 2*i9*i5 + 2*i9*i6 - 8*i9*i8
      - 6*sqr(i9) + 2*i10*i1 + 2*i10*i2 + 4*i10*i3 + 8*i10*i4 - 4*i10*i5 - 2*
     i10*i6 + 2*i10*i7 - 2*i10*i8 + 2*i10*i9 - 8*sqr(i10) =G= -700;

e10.. 6*i2*i1 - 7*sqr(i1) - 6*sqr(i2) - 10*i3*i1 + 6*i3*i2 - 8*sqr(i3) + 4*i4*
      i1 + 2*i4*i2 + 2*i4*i3 - 8*sqr(i4) - 2*i5*i1 + 2*i5*i2 + 8*i5*i4 - 4*sqr(
      i5) + 4*i6*i1 + 2*i6*i3 - 4*i6*i4 + 2*i6*i5 - 2*sqr(i6) - 2*i7*i1 + 2*i7*
      i2 - 4*i7*i3 + 2*i7*i4 + 2*i7*i5 + 2*i7*i6 - 6*sqr(i7) - 2*i8*i1 + 2*i8*
      i2 - 6*i8*i3 + 6*i8*i4 - 2*i8*i5 + 2*i8*i6 - 4*i8*i7 - 5*sqr(i8) + 4*i9*
      i1 - 4*i9*i2 - 10*i9*i4 + 6*i9*i5 - 2*i9*i6 + 2*i9*i7 + 4*i9*i8 - 6*sqr(
      i9) + 2*i10*i2 - 4*i10*i3 + 2*i10*i4 - 2*i10*i5 + 2*i10*i6 + 4*i10*i7 - 6
      *i10*i8 + 2*i10*i9 - 7*sqr(i10) =G= -360;

e11.. -(7*sqr(i1) + 6*sqr(i2) + 37.6*i1 + 19.6*i2 + 8*sqr(i3) - 6*i3*i1 + 4*i3*
      i2 - 5.6*i3 + 6*sqr(i4) + 2*i4*i1 + 2*i4*i3 - 26*i4 + 7*sqr(i5) - 4*i5*i1
       - 2*i5*i2 - 6*i5*i3 - 125*i5 + 4*sqr(i6) + 2*i6*i1 - 4*i6*i2 - 4*i6*i3
       - 2*i6*i4 + 6*i6*i5 - 79.6*i6 + 6*sqr(i7) - 2*i7*i1 - 6*i7*i2 - 2*i7*i3
       + 4*i7*i5 + 4*i7*i6 - 104.2*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 - 4.6*i8 + 8*sqr(i9) - 2*i9*i1
       - 4*i9*i2 + 4*i9*i3 + 4*i9*i4 - 4*i9*i5 - 4*i9*i6 + 8*i9*i7 + 4*i9*i8 - 
      22.8*i9 + 6*sqr(i10) - 4*i10*i1 - 6*i10*i2 + 2*i10*i3 - 4*i10*i4 + 2*i10*
      i5 + 2*i10*i6 - 2*i10*i7 - 4*i10*i8 - 2*i10*i9 + 9*i10) + 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;
i9.up = 200;
i10.up = 200;

* set non-default levels
i1.l = 100;
i2.l = 100;
i3.l = 100;
i4.l = 100;
i5.l = 100;
i6.l = 100;
i7.l = 100;
i8.l = 100;
i9.l = 100;
i10.l = 100;

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;


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