MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance nvs12

Formats ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)
-481.20000000 p1 ( gdx sol )
(infeas: 0)
Other points (infeas > 1e-08)  
Dual Bounds
-481.20000000 (ALPHAECP)
-481.20000000 (ANTIGONE)
-481.20000000 (BARON)
-481.20000000 (BONMIN)
-481.20000000 (COUENNE)
-481.20000020 (CPLEX)
-481.20000000 (GUROBI)
-481.20000000 (LINDO)
-481.20000000 (SCIP)
-481.20004800 (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/gupta12
Added to library 25 Jul 2002
Problem type IQCQP
#Variables 4
#Binary Variables 0
#Integer Variables 4
#Nonlinear Variables 4
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 4
Objective Sense min
Objective type quadratic
Objective curvature convex
#Nonzeros in Objective 4
#Nonlinear Nonzeros in Objective 4
#Constraints 4
#Linear Constraints 0
#Quadratic Constraints 4
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature convex
#Nonzeros in Jacobian 16
#Nonlinear Nonzeros in Jacobian 16
#Nonzeros in (Upper-Left) Hessian of Lagrangian 16
#Nonzeros in Diagonal of Hessian of Lagrangian 4
#Blocks in Hessian of Lagrangian 1
Minimal blocksize in Hessian of Lagrangian 4
Maximal blocksize in Hessian of Lagrangian 4
Average blocksize in Hessian of Lagrangian 4.0
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Minimal coefficient 2.0000e+00
Maximal coefficient 9.3200e+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
*          5        1        4        0        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*          5        1        0        4        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         21        1       20        0
*
*  Solve m using MINLP minimizing objvar;


Variables  i1,i2,i3,i4,objvar;

Integer Variables  i1,i2,i3,i4;

Equations  e1,e2,e3,e4,e5;


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 =G= -1100;

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 =G= -440;

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 =G= -310;

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 =G= -460;

e5.. -(7*sqr(i1) + 6*sqr(i2) - 20*i1 - 93.2*i2 + 8*sqr(i3) - 6*i3*i1 + 4*i3*i2
      - 67.2*i3 + 6*sqr(i4) + 2*i4*i1 + 2*i4*i3 - 36.6*i4) + objvar =E= 0;

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

* set non-default levels
i1.l = 1;
i2.l = 1;
i3.l = 1;
i4.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;


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