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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance nemhaus

Formatsⓘ	ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)ⓘ	31. p1 ( gdx sol ) (infeas: 0)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	31. (ANTIGONE) 31. (BARON) 31. (COUENNE) 31. (CPLEX) 31. (LINDO) 31. (SCIP)
Referencesⓘ	Carlson, R C and Nemhauser, G L, Scheduling to Minimize Interaction Cost, Operations Research, 14:1, 1966, 52-58.
Sourceⓘ	GAMS Model Library model nemhaus
Applicationⓘ	Job Scheduling
Added to libraryⓘ	31 Jul 2001
Problem typeⓘ	QP
#Variablesⓘ	5
#Binary Variablesⓘ	0
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	5
#Nonlinear Binary Variablesⓘ	0
#Nonlinear Integer Variablesⓘ	0
Objective Senseⓘ	min
Objective typeⓘ	quadratic
Objective curvatureⓘ	indefinite
#Nonzeros in Objectiveⓘ	5
#Nonlinear Nonzeros in Objectiveⓘ	5
#Constraintsⓘ	5
#Linear Constraintsⓘ	5
#Quadratic Constraintsⓘ	0
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ
Constraints curvatureⓘ	linear
#Nonzeros in Jacobianⓘ	5
#Nonlinear Nonzeros in Jacobianⓘ	0
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	18
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	0
#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+00
Maximal coefficientⓘ	6.0000e+00
Infeasibility of initial pointⓘ	1
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*          6        6        0        0        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*          6        6        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         11        6        5        0
*
*  Solve m using NLP minimizing objvar;


Variables  objvar,x2,x3,x4,x5,x6;

Positive Variables  x2,x3,x4,x5,x6;

Equations  e1,e2,e3,e4,e5,e6;


e1.. -(2*x2*x4 + 4*x2*x5 + 3*x2*x6 + 6*x3*x4 + 2*x3*x5 + 3*x3*x6 + 5*x4*x5 + 3*
     x4*x6 + 3*x5*x6) + objvar =E= 0;

e2..    x2 =E= 1;

e3..    x3 =E= 1;

e4..    x4 =E= 1;

e5..    x5 =E= 1;

e6..    x6 =E= 1;

Model m / all /;

m.limrow=0; m.limcol=0;
m.tolproj=0.0;

$if NOT '%gams.u1%' == '' $include '%gams.u1%'

$if not set NLP $set NLP NLP
Solve m using %NLP% minimizing objvar;