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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance nvs08

Formats ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)
23.44972735 p1 ( gdx sol )
(infeas: 0)
Other points (infeas > 1e-08)  
Dual Bounds
23.44972732 (ANTIGONE)
23.44972732 (BARON)
23.44972735 (COUENNE)
23.44972641 (LINDO)
23.44972734 (SCIP)
16.38976202 (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/gupta08
Added to library 25 Jul 2002
Problem type MINLP
#Variables 3
#Binary Variables 0
#Integer Variables 2
#Nonlinear Variables 3
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 2
Objective Sense min
Objective type quadratic
Objective curvature convex
#Nonzeros in Objective 3
#Nonlinear Nonzeros in Objective 3
#Constraints 3
#Linear Constraints 0
#Quadratic Constraints 1
#Polynomial Constraints 0
#Signomial Constraints 2
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature indefinite
#Nonzeros in Jacobian 9
#Nonlinear Nonzeros in Jacobian 4
#Nonzeros in (Upper-Left) Hessian of Lagrangian 3
#Nonzeros in Diagonal of Hessian of Lagrangian 3
#Blocks in Hessian of Lagrangian 3
Minimal blocksize in Hessian of Lagrangian 1
Maximal blocksize in Hessian of Lagrangian 1
Average blocksize in Hessian of Lagrangian 1.0
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Minimal coefficient 2.4004e-01
Maximal coefficient 4.0000e+00
Infeasibility of initial point 6
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
*          4        1        3        0        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*          4        2        0        2        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         13        6        7        0
*
*  Solve m using MINLP minimizing objvar;


Variables  i1,i2,x3,objvar;

Integer Variables  i1,i2;

Equations  e1,e2,e3,e4;


e1.. sqrt(x3) + i1 + 2*i2 =G= 10;

e2.. 0.240038406144983*sqr(i1) - i2 + 0.255036980362153*x3 =G= -3;

e3.. sqr(i2) - 1/(POWER(x3,3)*sqrt(x3)) - 4*i1 =G= -12;

e4.. -(sqr((-3) + i1) + sqr((-2) + i2) + sqr(4 + x3)) + objvar =E= 0;

* set non-default bounds
i1.up = 200;
i2.up = 200;
x3.lo = 0.001; x3.up = 200;

* set non-default levels
i1.l = 1;
i2.l = 1;
x3.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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