MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance nvs01

Formatsⓘ	ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)ⓘ	12.46966882 p1 ( gdx sol ) (infeas: 2e-12)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	12.46966882 (ANTIGONE) 12.46966882 (BARON) 12.46966882 (COUENNE) 12.46966882 (LINDO) 12.46966882 (SCIP) 0.00000000 (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/gupta01
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ⓘ	nonlinear
Objective curvatureⓘ	indefinite
#Nonzeros in Objectiveⓘ	2
#Nonlinear Nonzeros in Objectiveⓘ	2
#Constraintsⓘ	3
#Linear Constraintsⓘ	1
#Quadratic Constraintsⓘ	0
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	2
Operands in Gen. Nonlin. Functionsⓘ	div mul sqr sqrt
Constraints curvatureⓘ	indefinite
#Nonzeros in Jacobianⓘ	7
#Nonlinear Nonzeros in Jacobianⓘ	5
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	8
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	2
#Blocks in Hessian of Lagrangianⓘ	1
Minimal blocksize in Hessian of Lagrangianⓘ	3
Maximal blocksize in Hessian of Lagrangianⓘ	3
Average blocksize in Hessian of Lagrangianⓘ	3.0
#Semicontinuitiesⓘ	0
#Nonlinear Semicontinuitiesⓘ	0
#SOS type 1ⓘ	0
#SOS type 2ⓘ	0
Minimal coefficientⓘ	4.7124e-02
Maximal coefficientⓘ	1.8505e+04
Infeasibility of initial pointⓘ	9.561e+05
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*          4        2        2        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
*         10        3        7        0
*
*  Solve m using MINLP minimizing objvar;


Variables  i1,i2,x3,objvar;

Positive Variables  x3;

Integer Variables  i1,i2;

Equations  e1,e2,e3,e4;


e1.. 420.169404664517*sqrt(900 + sqr(i1)) - x3*i1*i2 =E= 0;

e2..  - x3 =G= -100;

e3.. (2960.87631843 + 18505.4769901875*sqr(i2))/(7200 + sqr(i1)) - x3 =G= 0;

e4.. -0.04712385*sqrt(900 + sqr(i1))*i2 + objvar =E= 0;

* set non-default bounds
i1.up = 200;
i2.up = 200;
x3.up = 100;

* set non-default levels
i1.l = 100;
i2.l = 100;
x3.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;