MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance ex2_1_10

Formatsⓘ	ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)ⓘ	49318.01796000 p1 ( gdx sol ) (infeas: 6e-14)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	49318.01791000 (ANTIGONE) 49318.01791000 (BARON) 49318.01787000 (COUENNE) 49318.01796000 (CPLEX) 49318.01796000 (GUROBI) 49318.01796000 (LINDO) 49318.01796000 (SCIP)
Referencesⓘ	Floudas, C A, Pardalos, Panos M, Adjiman, C S, Esposito, W R, Gumus, Zeynep H, Harding, S T, Klepeis, John L, Meyer, Clifford A, and Schweiger, C A, Handbook of Test Problems in Local and Global Optimization, Kluwer Academic Publishers, 1999.
Sourceⓘ	Test Problem ex2.1.10 of Chapter 2 of Floudas e.a. handbook
Added to libraryⓘ	31 Jul 2001
Problem typeⓘ	QP
#Variablesⓘ	20
#Binary Variablesⓘ	0
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	20
#Nonlinear Binary Variablesⓘ	0
#Nonlinear Integer Variablesⓘ	0
Objective Senseⓘ	min
Objective typeⓘ	quadratic
Objective curvatureⓘ	indefinite
#Nonzeros in Objectiveⓘ	20
#Nonlinear Nonzeros in Objectiveⓘ	20
#Constraintsⓘ	10
#Linear Constraintsⓘ	10
#Quadratic Constraintsⓘ	0
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ
Constraints curvatureⓘ	linear
#Nonzeros in Jacobianⓘ	200
#Nonlinear Nonzeros in Jacobianⓘ	0
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	20
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	20
#Blocks in Hessian of Lagrangianⓘ	20
Minimal blocksize in Hessian of Lagrangianⓘ	1
Maximal blocksize in Hessian of Lagrangianⓘ	1
Average blocksize in Hessian of Lagrangianⓘ	1.0
#Semicontinuitiesⓘ	0
#Nonlinear Semicontinuitiesⓘ	0
#SOS type 1ⓘ	0
#SOS type 2ⓘ	0
Minimal coefficientⓘ	5.0000e-01
Maximal coefficientⓘ	9.8000e+01
Infeasibility of initial pointⓘ	40.66
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*         11        1        0       10        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         21       21        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        221      201       20        0
*
*  Solve m using NLP minimizing objvar;


Variables  x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17,x18,x19
          ,x20,objvar;

Positive Variables  x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17
          ,x18,x19,x20;

Equations  e1,e2,e3,e4,e5,e6,e7,e8,e9,e10,e11;


e1.. -(0.5*(42*sqr(52 + x11) + 98*sqr(3 + x12) + 48*sqr((-81) + x13) + 91*sqr((
     -30) + x14) + 11*sqr(85 + x15) + 63*sqr((-68) + x16) + 61*sqr((-27) + x17)
      + 61*sqr(81 + x18) + 38*sqr((-97) + x19) + 26*sqr(73 + x20)) - 0.5*(63*
     sqr(19 + x1) + 15*sqr(27 + x2) + 44*sqr(23 + x3) + 91*sqr(53 + x4) + 45*
     sqr(42 + x5) + 50*sqr((-26) + x6) + 89*sqr(33 + x7) + 58*sqr(23 + x8) + 86
     *sqr((-41) + x9) + 82*sqr((-19) + x10))) + objvar =E= 0;

e2..    3*x1 + 5*x2 + 5*x3 + 6*x4 + 4*x5 + 4*x6 + 5*x7 + 6*x8 + 4*x9 + 4*x10
      + 8*x11 + 4*x12 + 2*x13 + x14 + x15 + x16 + 2*x17 + x18 + 7*x19 + 3*x20
      =L= 380;

e3..    5*x1 + 4*x2 + 5*x3 + 4*x4 + x5 + 4*x6 + 4*x7 + 2*x8 + 5*x9 + 2*x10
      + 3*x11 + 6*x12 + x13 + 7*x14 + 7*x15 + 5*x16 + 8*x17 + 7*x18 + 2*x19
      + x20 =L= 415;

e4..    x1 + 5*x2 + 2*x3 + 4*x4 + 7*x5 + 3*x6 + x7 + 5*x8 + 7*x9 + 6*x10 + x11
      + 7*x12 + 2*x13 + 4*x14 + 7*x15 + 5*x16 + 3*x17 + 4*x18 + x19 + 2*x20
      =L= 385;

e5..    3*x1 + 2*x2 + 6*x3 + 3*x4 + 2*x5 + x6 + 6*x7 + x8 + 7*x9 + 3*x10
      + 7*x11 + 7*x12 + 8*x13 + 2*x14 + 3*x15 + 4*x16 + 5*x17 + 8*x18 + x19
      + 2*x20 =L= 405;

e6..    6*x1 + 6*x2 + 6*x3 + 4*x4 + 5*x5 + 2*x6 + 2*x7 + 4*x8 + 3*x9 + 2*x10
      + 7*x11 + 5*x12 + 3*x13 + 6*x14 + 7*x15 + 5*x16 + 8*x17 + 4*x18 + 6*x19
      + 3*x20 =L= 470;

e7..    5*x1 + 5*x2 + 2*x3 + x4 + 3*x5 + 5*x6 + 5*x7 + 7*x8 + 4*x9 + 3*x10
      + 4*x11 + x12 + 7*x13 + 3*x14 + 8*x15 + 3*x16 + x17 + 6*x18 + 2*x19
      + 8*x20 =L= 415;

e8..    3*x1 + 6*x2 + 6*x3 + 3*x4 + x5 + 6*x6 + x7 + 6*x8 + 7*x9 + x10 + 4*x11
      + 3*x12 + x13 + 4*x14 + 3*x15 + 6*x16 + 4*x17 + 6*x18 + 5*x19 + 4*x20
      =L= 400;

e9..    x1 + 2*x2 + x3 + 7*x4 + 8*x5 + 7*x6 + 6*x7 + 5*x8 + 8*x9 + 7*x10
      + 2*x11 + 3*x12 + 5*x13 + 5*x14 + 4*x15 + 5*x16 + 4*x17 + 2*x18 + 2*x19
      + 8*x20 =L= 460;

e10..    8*x1 + 5*x2 + 2*x3 + 5*x4 + 3*x5 + 8*x6 + x7 + 3*x8 + 3*x9 + 5*x10
       + 4*x11 + 5*x12 + 5*x13 + 6*x14 + x15 + 7*x16 + x17 + 2*x18 + 2*x19
       + 4*x20 =L= 400;

e11..    x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9 + x10 + x11 + x12 + x13
       + x14 + x15 + x16 + x17 + x18 + x19 + x20 =L= 200;

* set non-default levels
x6.l = 4.348;
x14.l = 62.609;

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;