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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance st_rv8

Formatsⓘ	ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)ⓘ	-132.66162900 p1 ( gdx sol ) (infeas: 1e-13)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	-132.66162910 (ANTIGONE) -132.66162910 (BARON) -132.66162900 (COUENNE) -132.66162900 (CPLEX) -132.66162900 (GUROBI) -132.66162900 (LINDO) -132.66162960 (SCIP)
Referencesⓘ	Tawarmalani, M and Sahinidis, N V, Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming: Theory, Algorithms, Software, and Applications, Kluwer, 2002. Shectman, J P and Sahinidis, N V, A finite algorithm for global minimization of separable concave programs, Journal of Global Optimization, 12:1, 1998, 1-36. Shectman, J P, Finite Algorithms for Global Optimization of Concave Programs and General Quadratic Programs, PhD thesis, Department of Mechanical and Industrial Engineering, University of Illinois, Urbana Champagne, 1999.
Added to libraryⓘ	03 Sep 2002
Problem typeⓘ	QP
#Variablesⓘ	40
#Binary Variablesⓘ	0
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	40
#Nonlinear Binary Variablesⓘ	0
#Nonlinear Integer Variablesⓘ	0
Objective Senseⓘ	min
Objective typeⓘ	quadratic
Objective curvatureⓘ	concave
#Nonzeros in Objectiveⓘ	40
#Nonlinear Nonzeros in Objectiveⓘ	40
#Constraintsⓘ	20
#Linear Constraintsⓘ	20
#Quadratic Constraintsⓘ	0
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ
Constraints curvatureⓘ	linear
#Nonzeros in Jacobianⓘ	320
#Nonlinear Nonzeros in Jacobianⓘ	0
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	40
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	40
#Blocks in Hessian of Lagrangianⓘ	40
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-05
Maximal coefficientⓘ	9.0000e+00
Infeasibility of initial pointⓘ	0
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*         21        1        0       20        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         41       41        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        361      321       40        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,x21,x22,x23,x24,x25,x26,x27,x28,x29,x30,x31,x32,x33,x34,x35,x36
          ,x37,x38,x39,x40,objvar;

Positive Variables  x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17
          ,x18,x19,x20,x21,x22,x23,x24,x25,x26,x27,x28,x29,x30,x31,x32,x33,x34
          ,x35,x36,x37,x38,x39,x40;

Equations  e1,e2,e3,e4,e5,e6,e7,e8,e9,e10,e11,e12,e13,e14,e15,e16,e17,e18,e19
          ,e20,e21;


e1..    7*x1 + 4*x6 + 7*x7 + 6*x12 + 9*x13 + 2*x14 + x19 + 5*x20 + x25 + 5*x26
      + 3*x31 + 9*x32 + 5*x33 + x38 + x39 =L= 330;

e2..    4*x1 + 7*x2 + 7*x7 + 8*x8 + 9*x13 + 3*x14 + 6*x15 + 2*x20 + 6*x21
      + 5*x26 + 3*x27 + 4*x32 + 6*x33 + 6*x34 + 6*x39 + 3*x40 =L= 425;

e3..    x2 + 6*x3 + 8*x8 + 7*x9 + 9*x14 + 8*x15 + 8*x16 + 6*x21 + 5*x22 + 4*x27
      + 2*x28 + 4*x33 + 7*x34 + 9*x35 + 2*x40 =L= 430;

e4..    x3 + 5*x4 + 9*x9 + 6*x10 + 4*x15 + 9*x16 + 6*x17 + 7*x22 + 9*x23
      + 8*x28 + 3*x29 + 7*x34 + 4*x35 + 3*x36 =L= 405;

e5..    4*x4 + 7*x5 + 3*x10 + 6*x11 + 2*x16 + 8*x17 + 5*x18 + 2*x23 + 9*x24
      + 6*x29 + 4*x30 + 3*x35 + 6*x36 + 6*x37 =L= 355;

e6..    5*x5 + 5*x6 + 7*x11 + 4*x12 + 4*x17 + 6*x18 + 2*x19 + 4*x24 + 2*x25
      + x30 + 4*x31 + 4*x36 + 3*x37 + 4*x38 =L= 275;

e7..    2*x1 + 3*x6 + 3*x7 + 5*x12 + 9*x13 + 9*x18 + x19 + 4*x20 + 6*x25
      + 5*x26 + 3*x31 + 7*x32 + 3*x37 + 5*x38 + 4*x39 =L= 345;

e8..    9*x1 + 7*x2 + 3*x7 + 6*x8 + 7*x13 + 2*x14 + x19 + x20 + 4*x21 + 5*x26
      + 2*x27 + 6*x32 + 5*x33 + 4*x38 + 4*x39 + 3*x40 =L= 345;

e9..    6*x1 + 3*x2 + 4*x3 + 2*x8 + 7*x9 + 3*x14 + 7*x15 + 2*x20 + 3*x21
      + 2*x22 + 6*x27 + x28 + 6*x33 + 7*x34 + 9*x39 + 2*x40 =L= 350;

e10..    2*x2 + 8*x3 + 9*x4 + x9 + x10 + 6*x15 + x16 + 6*x21 + 7*x22 + 6*x23
       + 3*x28 + 2*x29 + 7*x34 + 6*x35 + 5*x40 =L= 350;

e11..    3*x3 + 6*x4 + 5*x5 + 6*x10 + 5*x11 + 8*x16 + 9*x17 + 6*x22 + 4*x23
       + x24 + 5*x29 + 2*x30 + 5*x35 + 4*x36 =L= 345;

e12..    3*x4 + 3*x5 + 9*x6 + 3*x11 + 8*x12 + 9*x17 + 4*x18 + 4*x23 + 3*x24
       + 6*x25 + 6*x30 + x31 + 6*x36 + 2*x37 =L= 335;

e13..    8*x5 + 2*x6 + 4*x7 + 8*x12 + 9*x13 + 3*x18 + 8*x19 + x24 + 8*x25
       + 8*x26 + 3*x31 + x32 + 5*x37 + 7*x38 =L= 375;

e14..    x1 + 9*x6 + x7 + 4*x8 + 9*x13 + 6*x14 + 6*x19 + 7*x20 + x25 + 5*x26
       + 7*x27 + x32 + 8*x33 + 9*x38 + 2*x39 =L= 380;

e15..    3*x1 + 9*x2 + 4*x7 + 2*x8 + x9 + 3*x14 + 9*x15 + 7*x20 + 7*x21 + 8*x26
       + 7*x27 + 5*x28 + 4*x33 + x34 + 6*x39 + 9*x40 =L= 425;

e16..    9*x2 + 6*x3 + 9*x8 + 5*x9 + 6*x10 + 6*x15 + 9*x16 + 5*x21 + 7*x22
       + 8*x27 + 7*x28 + x29 + x34 + 8*x35 + 4*x40 =L= 455;

e17..    9*x3 + 9*x4 + 4*x9 + 2*x10 + 7*x11 + 4*x16 + 8*x17 + 3*x22 + 2*x23
       + 2*x28 + 7*x29 + 3*x30 + 4*x35 + 9*x36 =L= 365;

e18..    5*x4 + 6*x5 + 8*x10 + 9*x11 + 6*x12 + 6*x17 + 4*x18 + 3*x23 + 3*x24
       + x29 + 9*x30 + 2*x31 + 4*x36 + 7*x37 =L= 365;

e19..    5*x5 + 7*x6 + 2*x11 + 8*x12 + x13 + 9*x18 + 8*x19 + 6*x24 + x25
       + 4*x30 + 9*x31 + 7*x32 + 4*x37 + 6*x38 =L= 385;

e20..    x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9 + x10 + x11 + x12 + x13
       + x14 + x15 + x16 + x17 + x18 + x19 + x20 + x21 + x22 + x23 + x24 + x25
       + x26 + x27 + x28 + x29 + x30 + x31 + x32 + x33 + x34 + x35 + x36 + x37
       + x38 + x39 + x40 =L= 400;

e21.. -(-0.0004*sqr(x1) - 0.0384*x1 - 0.00285*sqr(x2) - 0.3876*x2 - 0.00155*
      sqr(x3) - 0.1116*x3 - 0.0038*sqr(x4) - 0.4636*x4 - 0.0044*sqr(x5) - 0.044
      *x5 - 0.0046*sqr(x6) - 0.3588*x6 - 0.00085*sqr(x7) - 0.0272*x7 - 0.00165*
      sqr(x8) - 0.231*x8 - 0.0025*sqr(x9) - 0.27*x9 - 0.00385*sqr(x10) - 0.308*
      x10 - 0.00355*sqr(x11) - 0.3692*x11 - 0.0015*sqr(x12) - 0.288*x12 - 
      0.0037*sqr(x13) - 0.407*x13 - 0.00125*sqr(x14) - 0.1175*x14 - 0.00095*
      sqr(x15) - 0.1045*x15 - 0.0048*sqr(x16) - 0.1632*x16 - 0.0015*sqr(x17) - 
      0.135*x17 - 0.0037*sqr(x18) - 0.0666*x18 - 0.00125*sqr(x19) - 0.21*x19 - 
      0.00095*sqr(x20) - 0.1425*x20 - 0.0045*sqr(x21) - 0.882*x21 - 0.00245*
      sqr(x22) - 0.3283*x22 - 0.0004*sqr(x23) - 0.0648*x23 - 0.0048*sqr(x24) - 
      0.0864*x24 - 0.00485*sqr(x25) - 0.4753*x25 - 0.00025*sqr(x26) - 0.046*x26
       - 0.00435*sqr(x27) - 0.7917*x27 - 0.00365*sqr(x28) - 0.7008*x28 - 0.0002
      *sqr(x29) - 0.0384*x29 - 0.00205*sqr(x30) - 0.0164*x30 - 0.00165*sqr(x31)
       - 0.0891*x31 - 0.00175*sqr(x32) - 0.0945*x32 - 0.0048*sqr(x33) - 0.7296*
      x33 - 5e-5*sqr(x34) - 0.0023*x34 - 0.00155*sqr(x35) - 0.1488*x35 - 
      0.00015*sqr(x36) - 0.0189*x36 - 0.00245*sqr(x37) - 0.0343*x37 - 0.00095*
      sqr(x38) - 0.1045*x38 - 0.0038*sqr(x39) - 0.608*x39 - 0.0029*sqr(x40) - 
      0.0174*x40) + objvar =E= 0;

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;