MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance nvs09

Formatsⓘ	ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)ⓘ	-43.13433692 p1 ( gdx sol ) (infeas: 0)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	-43.13433692 (ANTIGONE) -43.13433692 (BARON) -43.13433692 (COUENNE) -43.13433692 (LINDO) -43.13433692 (SCIP) -81.00000000 (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/gupta09
Added to libraryⓘ	25 Jul 2002
Problem typeⓘ	INLP
#Variablesⓘ	10
#Binary Variablesⓘ	0
#Integer Variablesⓘ	10
#Nonlinear Variablesⓘ	10
#Nonlinear Binary Variablesⓘ	0
#Nonlinear Integer Variablesⓘ	10
Objective Senseⓘ	min
Objective typeⓘ	nonlinear
Objective curvatureⓘ	nonconcave
#Nonzeros in Objectiveⓘ	10
#Nonlinear Nonzeros in Objectiveⓘ	10
#Constraintsⓘ	0
#Linear Constraintsⓘ	0
#Quadratic Constraintsⓘ	0
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ	log mul sqr vcpower
Constraints curvatureⓘ	linear
#Nonzeros in Jacobianⓘ	0
#Nonlinear Nonzeros in Jacobianⓘ	0
#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-01
Maximal coefficientⓘ	1.0000e+01
Infeasibility of initial pointⓘ	0
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*          1        1        0        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
*         11        1       10        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;


e1.. -(sqr(log((-2) + i1)) + sqr(log(10 - i1)) + sqr(log((-2) + i2)) + sqr(log(
     10 - i2)) + sqr(log((-2) + i3)) + sqr(log(10 - i3)) + sqr(log((-2) + i4))
      + sqr(log(10 - i4)) + sqr(log((-2) + i5)) + sqr(log(10 - i5)) + sqr(log((
     -2) + i6)) + sqr(log(10 - i6)) + sqr(log((-2) + i7)) + sqr(log(10 - i7))
      + sqr(log((-2) + i8)) + sqr(log(10 - i8)) + sqr(log((-2) + i9)) + sqr(
     log(10 - i9)) + sqr(log((-2) + i10)) + sqr(log(10 - i10)) - (i1*i2*i3*i4*
     i5*i6*i7*i8*i9*i10)**0.2) + objvar =E= 0;

* set non-default bounds
i1.lo = 3; i1.up = 9;
i2.lo = 3; i2.up = 9;
i3.lo = 3; i3.up = 9;
i4.lo = 3; i4.up = 9;
i5.lo = 3; i5.up = 9;
i6.lo = 3; i6.up = 9;
i7.lo = 3; i7.up = 9;
i8.lo = 3; i8.up = 9;
i9.lo = 3; i9.up = 9;
i10.lo = 3; i10.up = 9;

* set non-default levels
i1.l = 5;
i2.l = 5;
i3.l = 5;
i4.l = 5;
i5.l = 5;
i6.l = 5;
i7.l = 5;
i8.l = 5;
i9.l = 5;
i10.l = 5;

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;