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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance: chakra

Formats ams gms mod nl osil
Primal Bounds
-179.13355790 p1 ( gdx sol )
(infeas: 1e-14)
Dual Bounds
-179.13357260 (ANTIGONE)
-179.13355800 (BARON)
-179.13355790 (COUENNE)
-179.13355790 (LINDO)
-179.13355790 (SCIP)
References Kendrick, D and Taylor, L, Numerical methods and Nonlinear Optimizing models for Economic Planning. In Chenery, Hollis B, Ed, Studies in Development Planning, Harvard University Press, 1971.
Source GAMS Model Library model chakra
Application Financial Optimization
Added to library 31 Jul 2001
Problem type NLP
#Variables 62
#Binary Variables 0
#Integer Variables 0
#Nonlinear Variables 41
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense min
Objective type signomial
Objective curvature convex
#Nonzeros in Objective 20
#Nonlinear Nonzeros in Objective 20
#Constraints 41
#Linear Constraints 20
#Quadratic Constraints 0
#Polynomial Constraints 0
#Signomial Constraints 21
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature indefinite
#Nonzeros in Jacobian 122
#Nonlinear Nonzeros in Jacobian 21
#Nonzeros in (Upper-Left) Hessian of Lagrangian 41
#Nonzeros in Diagonal of Hessian of Lagrangian 41
#Blocks in Hessian of Lagrangian 41
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
Infeasibility of initial point 1.137e-13
Sparsity Jacobian Sparsity of Objective Gradient and Jacobian
Sparsity Hessian of Lagrangian Sparsity of Hessian of Lagrangian

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*         42       42        0        0        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         63       63        0        0        0        0        0        0
*  FX      2
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        143      102       41        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,x41,x42,x43,x44,x45,x46,x47,x48,x49,x50,x51,x52,x53
          ,x54,x55,x56,x57,x58,x59,x60,x61,x62,objvar;

Equations  e1,e2,e3,e4,e5,e6,e7,e8,e9,e10,e11,e12,e13,e14,e15,e16,e17,e18,e19
          ,e20,e21,e22,e23,e24,e25,e26,e27,e28,e29,e30,e31,e32,e33,e34,e35,e36
          ,e37,e38,e39,e40,e41,e42;


e1..    x1 - x21 - 0.95*x42 + x43 =E= 0;

e2..    x2 - x22 - 0.95*x43 + x44 =E= 0;

e3..    x3 - x23 - 0.95*x44 + x45 =E= 0;

e4..    x4 - x24 - 0.95*x45 + x46 =E= 0;

e5..    x5 - x25 - 0.95*x46 + x47 =E= 0;

e6..    x6 - x26 - 0.95*x47 + x48 =E= 0;

e7..    x7 - x27 - 0.95*x48 + x49 =E= 0;

e8..    x8 - x28 - 0.95*x49 + x50 =E= 0;

e9..    x9 - x29 - 0.95*x50 + x51 =E= 0;

e10..    x10 - x30 - 0.95*x51 + x52 =E= 0;

e11..    x11 - x31 - 0.95*x52 + x53 =E= 0;

e12..    x12 - x32 - 0.95*x53 + x54 =E= 0;

e13..    x13 - x33 - 0.95*x54 + x55 =E= 0;

e14..    x14 - x34 - 0.95*x55 + x56 =E= 0;

e15..    x15 - x35 - 0.95*x56 + x57 =E= 0;

e16..    x16 - x36 - 0.95*x57 + x58 =E= 0;

e17..    x17 - x37 - 0.95*x58 + x59 =E= 0;

e18..    x18 - x38 - 0.95*x59 + x60 =E= 0;

e19..    x19 - x39 - 0.95*x60 + x61 =E= 0;

e20..    x20 - x40 - 0.95*x61 + x62 =E= 0;

e21.. -0.560877056310648*x42**0.75 + x21 =E= 0;

e22.. -0.569991308475696*x43**0.75 + x22 =E= 0;

e23.. -0.579253667238426*x44**0.75 + x23 =E= 0;

e24.. -0.58866653933105*x45**0.75 + x24 =E= 0;

e25.. -0.59823237059518*x46**0.75 + x25 =E= 0;

e26.. -0.607953646617352*x47**0.75 + x26 =E= 0;

e27.. -0.617832893374884*x48**0.75 + x27 =E= 0;

e28.. -0.627872677892226*x49**0.75 + x28 =E= 0;

e29.. -0.638075608907974*x50**0.75 + x29 =E= 0;

e30.. -0.648444337552729*x51**0.75 + x30 =E= 0;

e31.. -0.658981558037961*x52**0.75 + x31 =E= 0;

e32.. -0.669690008356078*x53**0.75 + x32 =E= 0;

e33.. -0.680572470991864*x54**0.75 + x33 =E= 0;

e34.. -0.691631773645482*x55**0.75 + x34 =E= 0;

e35.. -0.702870789967221*x56**0.75 + x35 =E= 0;

e36.. -0.714292440304189*x57**0.75 + x36 =E= 0;

e37.. -0.725899692459132*x58**0.75 + x37 =E= 0;

e38.. -0.737695562461593*x59**0.75 + x38 =E= 0;

e39.. -0.749683115351594*x60**0.75 + x39 =E= 0;

e40.. -0.761865465976057*x61**0.75 + x40 =E= 0;

e41.. -0.774245779798168*x62**0.75 + x41 =E= 0;

e42.. -(10*x1**0.1 + 9.70873786407767*x2**0.1 + 9.42595909133755*x3**0.1 + 
      9.1514165935316*x4**0.1 + 8.88487047915689*x5**0.1 + 8.62608784384164*x6
      **0.1 + 8.37484256683654*x7**0.1 + 8.13091511343354*x8**0.1 + 
      7.89409234313936*x9**0.1 + 7.66416732343627*x10**0.1 + 7.44093914896725*
      x11**0.1 + 7.22421276598762*x12**0.1 + 7.01379880192973*x13**0.1 + 
      6.80951339993178*x14**0.1 + 6.61117805818619*x15**0.1 + 6.41861947396717*
      x16**0.1 + 6.23166939220114*x17**0.1 + 6.05016445844771*x18**0.1 + 
      5.87394607616282*x19**0.1 + 5.70286026811925*x20**0.1) - objvar =E= 0;

* set non-default bounds
x1.lo = 1;
x2.lo = 1;
x3.lo = 1;
x4.lo = 1;
x5.lo = 1;
x6.lo = 1;
x7.lo = 1;
x8.lo = 1;
x9.lo = 1;
x10.lo = 1;
x11.lo = 1;
x12.lo = 1;
x13.lo = 1;
x14.lo = 1;
x15.lo = 1;
x16.lo = 1;
x17.lo = 1;
x18.lo = 1;
x19.lo = 1;
x20.lo = 1;
x21.fx = 4.275;
x22.lo = 1;
x23.lo = 1;
x24.lo = 1;
x25.lo = 1;
x26.lo = 1;
x27.lo = 1;
x28.lo = 1;
x29.lo = 1;
x30.lo = 1;
x31.lo = 1;
x32.lo = 1;
x33.lo = 1;
x34.lo = 1;
x35.lo = 1;
x36.lo = 1;
x37.lo = 1;
x38.lo = 1;
x39.lo = 1;
x40.lo = 1;
x41.fx = 13.7105041437099;
x42.lo = 1;
x43.lo = 1;
x44.lo = 1;
x45.lo = 1;
x46.lo = 1;
x47.lo = 1;
x48.lo = 1;
x49.lo = 1;
x50.lo = 1;
x51.lo = 1;
x52.lo = 1;
x53.lo = 1;
x54.lo = 1;
x55.lo = 1;
x56.lo = 1;
x57.lo = 1;
x58.lo = 1;
x59.lo = 1;
x60.lo = 1;
x61.lo = 1;
x62.lo = 1;

* set non-default levels
x1.l = 2.65787165646338;
x2.l = 2.82088780167558;
x3.l = 2.99388978021114;
x4.l = 3.17748858499683;
x5.l = 3.37233255315755;
x6.l = 3.57910964624529;
x7.l = 3.79854986956959;
x8.l = 4.03142783910829;
x9.l = 4.27856550499249;
x10.l = 4.54083504110911;
x11.l = 4.81916191094403;
x12.l = 5.11452812040594;
x13.l = 5.42797566902516;
x14.l = 5.76061021161472;
x15.l = 6.11360494321835;
x16.l = 6.48820472094886;
x17.l = 6.88573043715017;
x18.l = 7.30758365919495;
x19.l = 7.75525155216026;
x20.l = 8.23031210161431;
x22.l = 4.5315;
x23.l = 4.80339;
x24.l = 5.0915934;
x25.l = 5.397089004;
x26.l = 5.72091434424;
x27.l = 6.0641692048944;
x28.l = 6.42801935718807;
x29.l = 6.81370051861935;
x30.l = 7.22252254973651;
x31.l = 7.6558739027207;
x32.l = 8.11522633688395;
x33.l = 8.60213991709698;
x34.l = 9.1182683121228;
x35.l = 9.66536441085017;
x36.l = 10.2452862755012;
x37.l = 10.8600034520313;
x38.l = 11.5116036591531;
x39.l = 12.2022998787023;
x40.l = 12.9344378714245;
x42.l = 15;
x43.l = 15.8671283435366;
x44.l = 16.7843841246842;
x45.l = 17.7546651382389;
x46.l = 18.7810366963301;
x47.l = 19.866741312356;
x48.l = 21.0152089447329;
x49.l = 22.2300678328211;
x50.l = 23.5151559592598;
x51.l = 24.8745331749237;
x52.l = 26.3124940248049;
x53.l = 27.8335813153413;
x54.l = 29.4426004660523;
x55.l = 31.1446346908215;
x56.l = 32.9450610567885;
x57.l = 34.8495674715809;
x58.l = 36.8641706525542;
x59.l = 38.9952351348075;
x60.l = 41.2494933780253;
x61.l = 43.6340670356661;
x62.l = 46.156489453693;

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;


Last updated: 2018-05-28 Git hash: ac4a64c1
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