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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance hmittelman

Formatsⓘ	ams gms mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)ⓘ	13.00000000 p1 ( gdx sol ) (infeas: 0)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	13.00000000 (ANTIGONE) 13.00000000 (BARON) 13.00000000 (COUENNE) 13.00000000 (LINDO) 13.00000000 (SCIP) 0.00000000 (SHOT)
Sourceⓘ	MacMINLP model mittelman.mod
Added to libraryⓘ	01 May 2001
Problem typeⓘ	BNLP
#Variablesⓘ	16
#Binary Variablesⓘ	16
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	16
#Nonlinear Binary Variablesⓘ	16
#Nonlinear Integer Variablesⓘ	0
Objective Senseⓘ	min
Objective typeⓘ	polynomial
Objective curvatureⓘ	indefinite
#Nonzeros in Objectiveⓘ	15
#Nonlinear Nonzeros in Objectiveⓘ	15
#Constraintsⓘ	7
#Linear Constraintsⓘ	0
#Quadratic Constraintsⓘ	0
#Polynomial Constraintsⓘ	7
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ
Constraints curvatureⓘ	indefinite
#Nonzeros in Jacobianⓘ	107
#Nonlinear Nonzeros in Jacobianⓘ	107
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	110
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	0
#Blocks in Hessian of Lagrangianⓘ	1
Minimal blocksize in Hessian of Lagrangianⓘ	16
Maximal blocksize in Hessian of Lagrangianⓘ	16
Average blocksize in Hessian of Lagrangianⓘ	16.0
#Semicontinuitiesⓘ	0
#Nonlinear Semicontinuitiesⓘ	0
#SOS type 1ⓘ	0
#SOS type 2ⓘ	0
Minimal coefficientⓘ	2.0000e+00
Maximal coefficientⓘ	1.5000e+01
Infeasibility of initial pointⓘ	6.343
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*          8        1        0        7        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         17        1       16        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        123        1      122        0
*
*  Solve m using MINLP minimizing objvar;


Variables  b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,b12,b13,b14,b15,b16,objvar;

Binary Variables  b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,b12,b13,b14,b15,b16;

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


e1.. -(10*b5*b7*b9*b10*b14*b15*b16 + 7*b1*b2*b3*b4*b8*b11 + b3*b4*b6*b7*b8 + 12
     *b3*b4*b8*b11 + 8*b6*b7*b8*b12 + 3*b6*b7*b9*b14*b16 + b9*b10*b14*b16 + 5*
     b5*b10*b14*b15*b16 + 3*b1*b2*b11*b12) + objvar =E= 0;

e2.. 3*b5*b7*b9*b10*b14*b15*b16 - 12*b1*b2*b3*b4*b8*b11 - 8*b3*b4*b6*b7*b8 + b3
     *b4*b8*b11 - 7*b1*b2*b11*b12 + 2*b13*b14*b15*b16 =L= -2;

e3.. b1*b2*b3*b4*b8*b11 - 10*b3*b4*b6*b7*b8 - 5*b6*b7*b8*b12 + b6*b7*b9*b14*b16
      + 7*b9*b10*b14*b16 + b5*b10*b14*b15*b16 =L= -1;

e4.. 5*b5*b7*b9*b10*b14*b15*b16 - 3*b1*b2*b3*b4*b8*b11 - b3*b4*b6*b7*b8 - 2*b5*
     b10*b14*b15*b16 + b13*b14*b15*b16 =L= -1;

e5.. 3*b1*b2*b3*b4*b8*b11 - 5*b5*b7*b9*b10*b14*b15*b16 + b3*b4*b6*b7*b8 + 2*b5*
     b10*b14*b15*b16 - b13*b14*b15*b16 =L= 1;

e6.. (-4*b3*b4*b6*b7*b8) - 2*b3*b4*b8*b11 - 5*b6*b7*b9*b14*b16 + b9*b10*b14*b16
      - 9*b5*b10*b14*b15*b16 - 2*b1*b2*b11*b12 =L= -3;

e7.. 9*b1*b2*b3*b4*b8*b11 - 12*b3*b4*b8*b11 - 7*b6*b7*b8*b12 + 6*b6*b7*b9*b14*
     b16 + 2*b5*b10*b14*b15*b16 - 15*b1*b2*b11*b12 + 3*b13*b14*b15*b16 =L= -7;

e8.. 5*b1*b2*b3*b4*b8*b11 - 8*b5*b7*b9*b10*b14*b15*b16 + 2*b3*b4*b6*b7*b8 - 7*
     b3*b4*b8*b11 - b6*b7*b8*b12 - 5*b9*b10*b14*b16 - 10*b1*b2*b11*b12 =L= -1;

* set non-default levels
b1.l = 0.171747132;
b2.l = 0.843266708;
b3.l = 0.550375356;
b4.l = 0.301137904;
b5.l = 0.292212117;
b6.l = 0.224052867;
b7.l = 0.349830504;
b8.l = 0.998117627;
b9.l = 0.578733378;
b10.l = 0.991133039;
b11.l = 0.130692483;
b12.l = 0.639718759;
b13.l = 0.159517864;
b14.l = 0.250080533;
b15.l = 0.668928609;
b16.l = 0.435356381;

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;