MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance nvs11

Formatsⓘ	ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)ⓘ	-431.00000000 p1 ( gdx sol ) (infeas: 0)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	-431.00000000 (ALPHAECP) -431.00000000 (ANTIGONE) -431.00000000 (BARON) -431.00000000 (BONMIN) -431.00000000 (COUENNE) -431.00000010 (CPLEX) -431.00000000 (GUROBI) -431.00000000 (LINDO) -431.00000000 (SCIP) -431.00000090 (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/gupta11
Added to libraryⓘ	25 Jul 2002
Problem typeⓘ	IQCQP
#Variablesⓘ	3
#Binary Variablesⓘ	0
#Integer Variablesⓘ	3
#Nonlinear Variablesⓘ	3
#Nonlinear Binary Variablesⓘ	0
#Nonlinear Integer Variablesⓘ	3
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ⓘ	3
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ
Constraints curvatureⓘ	convex
#Nonzeros in Jacobianⓘ	9
#Nonlinear Nonzeros in Jacobianⓘ	9
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	9
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	3
#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ⓘ	2.0000e+00
Maximal coefficientⓘ	9.3200e+01
Infeasibility of initial pointⓘ	0
Sparsity Jacobianⓘ
Sparsity 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        1        0        3        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         13        1       12        0
*
*  Solve m using MINLP minimizing objvar;


Variables  i1,i2,i3,objvar;

Integer Variables  i1,i2,i3;

Equations  e1,e2,e3,e4;


e1.. (-9*sqr(i1)) - 10*i1*i2 - 8*sqr(i2) - 5*sqr(i3) - 6*i3*i1 - 10*i3*i2
      =G= -1000;

e2.. (-6*sqr(i1)) - 8*i1*i2 - 6*sqr(i2) - 4*sqr(i3) - 2*i3*i1 - 2*i3*i2
      =G= -550;

e3.. (-9*sqr(i1)) - 6*sqr(i2) - 8*sqr(i3) + 2*i2*i1 + 2*i3*i2 =G= -340;

e4.. -(7*sqr(i1) + 6*sqr(i2) - 15.8*i1 - 93.2*i2 + 8*sqr(i3) - 6*i3*i1 + 4*i3*
     i2 - 63*i3) + objvar =E= 0;

* set non-default bounds
i1.up = 200;
i2.up = 200;
i3.up = 200;

* set non-default levels
i1.l = 1;
i2.l = 1;
i3.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;