MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance nvs02

Formatsⓘ	ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)ⓘ	5.98462763 p1 ( gdx sol ) (infeas: 2e-15) 5.96418452 p2 ( gdx sol ) (infeas: 1e-14)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	5.96418452 (ANTIGONE) 5.96418452 (BARON) 5.96418452 (COUENNE) 5.96418452 (GUROBI) 5.96418452 (LINDO) 5.96418452 (SCIP) 5.92078590 (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/gupta02
Added to libraryⓘ	25 Jul 2002
Problem typeⓘ	MIQCQP
#Variablesⓘ	8
#Binary Variablesⓘ	0
#Integer Variablesⓘ	5
#Nonlinear Variablesⓘ	5
#Nonlinear Binary Variablesⓘ	0
#Nonlinear Integer Variablesⓘ	5
Objective Senseⓘ	min
Objective typeⓘ	quadratic
Objective curvatureⓘ	indefinite
#Nonzeros in Objectiveⓘ	3
#Nonlinear Nonzeros in Objectiveⓘ	3
#Constraintsⓘ	3
#Linear Constraintsⓘ	0
#Quadratic Constraintsⓘ	3
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ
Constraints curvatureⓘ	indefinite
#Nonzeros in Jacobianⓘ	16
#Nonlinear Nonzeros in Jacobianⓘ	13
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	15
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	1
#Blocks in Hessian of Lagrangianⓘ	1
Minimal blocksize in Hessian of Lagrangianⓘ	5
Maximal blocksize in Hessian of Lagrangianⓘ	5
Average blocksize in Hessian of Lagrangianⓘ	5.0
#Semicontinuitiesⓘ	0
#Nonlinear Semicontinuitiesⓘ	0
#SOS type 1ⓘ	0
#SOS type 2ⓘ	0
Minimal coefficientⓘ	1.0000e-04
Maximal coefficientⓘ	3.7293e+01
Infeasibility of initial pointⓘ	126.4
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*          4        4        0        0        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*          9        4        0        5        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         20        4       16        0
*
*  Solve m using MINLP minimizing objvar;


Variables  i1,i2,i3,i4,i5,x6,x7,x8,objvar;

Positive Variables  x6;

Integer Variables  i1,i2,i3,i4,i5;

Equations  e1,e2,e3,e4;


e1.. -(0.0056858*i2*i5 + 0.0006262*i1*i4 - 0.0022053*i3*i5) + x6 =E= 85.334407;

e2.. -(0.0071317*i2*i5 + 0.0029955*i1*i2 + 0.0021813*sqr(i3)) + x7 =E= 80.51249
     ;

e3.. -(0.0047026*i3*i5 + 0.0012547*i1*i3 + 0.0019085*i3*i4) + x8 =E= 9.300961;

e4.. -9.99999999999999e-5*(5.3578547*sqr(i3) + 0.8356891*i1*i5 + 37.293239*i1)
      + objvar =E= 5.9207859;

* set non-default bounds
i1.up = 200;
i2.up = 200;
i3.up = 200;
i4.up = 200;
i5.up = 200;
x6.up = 92;
x7.lo = 90; x7.up = 110;
x8.lo = 20; x8.up = 25;

* set non-default levels
i1.l = 100;
i2.l = 100;
i3.l = 100;
i4.l = 100;
i5.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;