MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance nvs05

Formatsⓘ	ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)ⓘ	5.47093411 p1 ( gdx sol ) (infeas: 2e-12)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	5.47093410 (ANTIGONE) 5.47093411 (BARON) 5.47093411 (COUENNE) 5.47093411 (LINDO) 5.47093410 (SCIP) 0.67402220 (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/gupta05
Added to libraryⓘ	25 Jul 2002
Problem typeⓘ	MINLP
#Variablesⓘ	8
#Binary Variablesⓘ	0
#Integer Variablesⓘ	2
#Nonlinear Variablesⓘ	8
#Nonlinear Binary Variablesⓘ	0
#Nonlinear Integer Variablesⓘ	2
Objective Senseⓘ	min
Objective typeⓘ	polynomial
Objective curvatureⓘ	indefinite
#Nonzeros in Objectiveⓘ	4
#Nonlinear Nonzeros in Objectiveⓘ	4
#Constraintsⓘ	9
#Linear Constraintsⓘ	1
#Quadratic Constraintsⓘ	0
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	4
#General Nonlinear Constraintsⓘ	4
Operands in Gen. Nonlin. Functionsⓘ	div mul power sqr sqrt
Constraints curvatureⓘ	indefinite
#Nonzeros in Jacobianⓘ	26
#Nonlinear Nonzeros in Jacobianⓘ	20
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	30
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	8
#Blocks in Hessian of Lagrangianⓘ	2
Minimal blocksize in Hessian of Lagrangianⓘ	3
Maximal blocksize in Hessian of Lagrangianⓘ	5
Average blocksize in Hessian of Lagrangianⓘ	4.0
#Semicontinuitiesⓘ	0
#Nonlinear Semicontinuitiesⓘ	0
#SOS type 1ⓘ	0
#SOS type 2ⓘ	0
Minimal coefficientⓘ	2.0474e-02
Maximal coefficientⓘ	1.0000e+15
Infeasibility of initial pointⓘ	4.74e+05
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*         10        5        5        0        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*          9        7        0        2        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         31        7       24        0
*
*  Solve m using MINLP minimizing objvar;


Variables  i1,i2,x3,x4,x5,x6,x7,x8,objvar;

Integer Variables  i1,i2;

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


e1.. -4243.28147100424/(x3*x4) + x5 =E= 0;

e2.. -sqrt(0.25*sqr(x4) + sqr(0.5*i1 + 0.5*x3)) + x7 =E= 0;

e3.. -(59405.9405940594 + 2121.64073550212*x4)*x7/(x3*x4*(0.0833333333333333*
     sqr(x4) + sqr(0.5*i1 + 0.5*x3))) + x6 =E= 0;

e4.. -0.5*x4/x7 + x8 =E= 0;

e5.. -sqrt(sqr(x5) + 2*x5*x6*x8 + sqr(x6)) =G= -13600;

e6.. -504000/(sqr(i1)*i2) =G= -30000;

e7..    i2 - x3 =G= 0;

e8.. 0.0204744897959184*sqrt(1e15*POWER(i2,3)*i1*i1*POWER(i2,3))*(1 - 
     0.0282346219657891*i1) =G= 6000;

e9.. -0.21952/(POWER(i1,3)*i2) =G= -0.25;

e10.. -(1.10471*sqr(x3)*x4 + 0.04811*i1*i2*(14 + x4)) + objvar =E= 0;

* set non-default bounds
i1.lo = 1; i1.up = 200;
i2.lo = 1; i2.up = 200;
x3.lo = 0.01; x3.up = 200;
x4.lo = 0.01; x4.up = 200;

* set non-default levels
x3.l = 1;
x4.l = 1;
x5.l = 1;
x6.l = 1;
x7.l = 2;
x8.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;