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Instance: etamac

Formats ams gms mod nl osil
Primal Bounds
-15.29467564 p1 ( gdx sol )
(infeas: 1e-10)
Dual Bounds
-15.83529486 (ANTIGONE)
-16.49103820 (BARON)
-18.38730842 (COUENNE)
-16.42980221 (LINDO)
References Manne, Alan S, ETA-MACRO: A Model of Energy-Economy Interactions. In Hitch, Charles J, Ed, Modeling Energy-Economy Interactions: Five Approaches, Resources for the Future, Washington, DC, 1977.
Source GAMS Model Library model etamac
Application Energy
Added to library 31 Jul 2001
Problem type NLP
#Variables 97
#Binary Variables 0
#Integer Variables 0
#Nonlinear Variables 35
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense min
Objective type nonlinear
Objective curvature convex
#Nonzeros in Objective 9
#Nonlinear Nonzeros in Objective 9
#Constraints 70
#Linear Constraints 61
#Quadratic Constraints 0
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 9
Operands in Gen. Nonlin. Functions mul vcpower log
Constraints curvature indefinite
#Nonzeros in Jacobian 216
#Nonlinear Nonzeros in Jacobian 26
#Nonzeros in (Upper-Left) Hessian of Lagrangian 85
#Nonzeros in Diagonal of Hessian of Lagrangian 35
#Blocks in Hessian of Lagrangian 18
Minimal blocksize in Hessian of Lagrangian 1
Maximal blocksize in Hessian of Lagrangian 3
Average blocksize in Hessian of Lagrangian 1.944444
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Infeasibility of initial point 2814
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
*         71       70        0        1        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         98       98        0        0        0        0        0        0
*  FX      1
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        226      191       35        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,x63,x64,x65,x66,x67,x68,x69,x70
          ,x71,x72,x73,x74,x75,x76,x77,x78,x79,x80,x81,x82,x83,x84,x85,x86,x87
          ,x88,x89,x90,x91,x92,x93,x94,x95,x96,x97,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,e43,e44,e45,e46,e47,e48,e49,e50,e51,e52,e53
          ,e54,e55,e56,e57,e58,e59,e60,e61,e62,e63,e64,e65,e66,e67,e68,e69,e70
          ,e71;


e1..    x10 - 4.91287681*x80 =E= 0;

e2..    x11 - 4.91287681*x81 =E= 0;

e3..    x12 - 4.91287681*x82 =E= 0;

e4..    x13 - 4.91287681*x83 =E= 0;

e5..    x14 - 4.91287681*x84 =E= 0;

e6..    x15 - 4.91287681*x85 =E= 0;

e7..    x16 - 4.91287681*x86 =E= 0;

e8..    x17 - 4.91287681*x87 =E= 0;

e9.. -(0.820744282617518*x10**(-0.342222222222222) + 0.306708090151268*x45**(-
     0.427777777777778)*x63**(-0.794444444444445))**(-0.818181818181818) + x27
      =E= 0;

e10.. -(0.7206494796327*x11**(-0.342222222222222) + 0.306708090151268*x46**(-
      0.427777777777778)*x64**(-0.794444444444445))**(-0.818181818181818) + x28
       =E= 0;

e11.. -(0.632761852252708*x12**(-0.342222222222222) + 0.306708090151268*x47**(-
      0.427777777777778)*x65**(-0.794444444444445))**(-0.818181818181818) + x29
       =E= 0;

e12.. -(0.555592660485018*x13**(-0.342222222222222) + 0.306708090151268*x48**(-
      0.427777777777778)*x66**(-0.794444444444445))**(-0.818181818181818) + x30
       =E= 0;

e13.. -(0.487834725317074*x14**(-0.342222222222222) + 0.306708090151268*x49**(-
      0.427777777777778)*x67**(-0.794444444444445))**(-0.818181818181818) + x31
       =E= 0;

e14.. -(0.428340286240339*x15**(-0.342222222222222) + 0.306708090151268*x50**(-
      0.427777777777778)*x68**(-0.794444444444445))**(-0.818181818181818) + x32
       =E= 0;

e15.. -(0.376101559185243*x16**(-0.342222222222222) + 0.306708090151268*x51**(-
      0.427777777777778)*x69**(-0.794444444444445))**(-0.818181818181818) + x33
       =E= 0;

e16.. -(0.330233665535262*x17**(-0.342222222222222) + 0.306708090151268*x52**(-
      0.427777777777778)*x70**(-0.794444444444445))**(-0.818181818181818) + x34
       =E= 0;

e17..  - x35 + x44 =E= -2.038431744;

e18..    0.8153726976*x35 - x36 + x45 =E= 0;

e19..    0.8153726976*x36 - x37 + x46 =E= 0;

e20..    0.8153726976*x37 - x38 + x47 =E= 0;

e21..    0.8153726976*x38 - x39 + x48 =E= 0;

e22..    0.8153726976*x39 - x40 + x49 =E= 0;

e23..    0.8153726976*x40 - x41 + x50 =E= 0;

e24..    0.8153726976*x41 - x42 + x51 =E= 0;

e25..    0.8153726976*x42 - x43 + x52 =E= 0;

e26..  - x53 + x62 =E= -40.76863488;

e27..    0.8153726976*x53 - x54 + x63 =E= 0;

e28..    0.8153726976*x54 - x55 + x64 =E= 0;

e29..    0.8153726976*x55 - x56 + x65 =E= 0;

e30..    0.8153726976*x56 - x57 + x66 =E= 0;

e31..    0.8153726976*x57 - x58 + x67 =E= 0;

e32..    0.8153726976*x58 - x59 + x68 =E= 0;

e33..    0.8153726976*x59 - x60 + x69 =E= 0;

e34..    0.8153726976*x60 - x61 + x70 =E= 0;

e35..  - 0.8153726976*x1 + x2 - x10 =E= 0;

e36..  - 0.8153726976*x2 + x3 - x11 =E= 0;

e37..  - 0.8153726976*x3 + x4 - x12 =E= 0;

e38..  - 0.8153726976*x4 + x5 - x13 =E= 0;

e39..  - 0.8153726976*x5 + x6 - x14 =E= 0;

e40..  - 0.8153726976*x6 + x7 - x15 =E= 0;

e41..  - 0.8153726976*x7 + x8 - x16 =E= 0;

e42..  - 0.8153726976*x8 + x9 - x17 =E= 0;

e43.. -(0.612508399277048 + 0.306708090151268*x44**(-0.427777777777778)*x62**(-
      0.794444444444445))**(-0.818181818181818) + x18 =E= 3.4653339648;

e44..  - 0.8153726976*x18 + x19 - x27 =E= 0;

e45..  - 0.8153726976*x19 + x20 - x28 =E= 0;

e46..  - 0.8153726976*x20 + x21 - x29 =E= 0;

e47..  - 0.8153726976*x21 + x22 - x30 =E= 0;

e48..  - 0.8153726976*x22 + x23 - x31 =E= 0;

e49..  - 0.8153726976*x23 + x24 - x32 =E= 0;

e50..  - 0.8153726976*x24 + x25 - x33 =E= 0;

e51..  - 0.8153726976*x25 + x26 - x34 =E= 0;

e52..  - 52.550502505*x35 - 4.9683636144*x53 + 1000*x89 =E= 0;

e53..  - 55.2311062705602*x36 - 5.48547488997641*x54 + 1000*x90 =E= 0;

e54..  - 58.0484477684999*x37 - 6.05640752245858*x55 + 1000*x91 =E= 0;

e55..  - 61.0095019973984*x38 - 6.68676328190259*x56 + 1000*x92 =E= 0;

e56..  - 64.1215997508617*x39 - 7.38272697509128*x57 + 1000*x93 =E= 0;

e57..  - 67.3924457666453*x40 - 8.15112712846509*x58 + 1000*x94 =E= 0;

e58..  - 70.8301378015635*x41 - 8.99950298698105*x59 + 1000*x95 =E= 0;

e59..  - 74.4431866794111*x42 - 9.93617848626683*x60 + 1000*x96 =E= 0;

e60..  - 78.2405373615315*x43 - 10.970343923856*x61 + 1000*x97 =E= 0;

e61..    x18 - x71 - x80 - x89 =E= 0;

e62..    x19 - x72 - x81 - x90 =E= 0;

e63..    x20 - x73 - x82 - x91 =E= 0;

e64..    x21 - x74 - x83 - x92 =E= 0;

e65..    x22 - x75 - x84 - x93 =E= 0;

e66..    x23 - x76 - x85 - x94 =E= 0;

e67..    x24 - x77 - x86 - x95 =E= 0;

e68..    x25 - x78 - x87 - x96 =E= 0;

e69..    x26 - x79 - x88 - x97 =E= 0;

e70..    0.07*x9 - x88 =L= 0;

e71.. -(0.8153726976*log(x71) + 0.664832635991501*log(x72) + 0.542086379860909*
      log(x73) + 0.442002433879407*log(x74) + 0.360396716858018*log(x75) + 
      0.293857643230706*log(x76) + 0.239603499271399*log(x77) + 
      0.19536615155532*log(x78) + 3.98240565033479*log(x79)) - objvar =E= 0;

* set non-default bounds
x1.fx = 12.32657617084;
x2.lo = 10.9;
x3.lo = 10.9;
x4.lo = 10.9;
x5.lo = 10.9;
x6.lo = 10.9;
x7.lo = 10.9;
x8.lo = 10.9;
x9.lo = 10.9;
x10.lo = 1.0317041301;
x11.lo = 1.0317041301;
x12.lo = 1.0317041301;
x13.lo = 1.0317041301;
x14.lo = 1.0317041301;
x15.lo = 1.0317041301;
x16.lo = 1.0317041301;
x17.lo = 1.0317041301;
x18.lo = 4.25;
x19.lo = 4.25;
x20.lo = 4.25;
x21.lo = 4.25;
x22.lo = 4.25;
x23.lo = 4.25;
x24.lo = 4.25;
x25.lo = 4.25;
x26.lo = 4.25;
x27.lo = 0.508311836408595;
x28.lo = 0.589272733608307;
x29.lo = 0.683128602764001;
x30.lo = 0.79193327859709;
x31.lo = 0.918067718453005;
x32.lo = 1.06429210445432;
x33.lo = 1.23380624417608;
x34.lo = 1.43031959158279;
x35.lo = 2.5;
x36.lo = 2.5;
x37.lo = 2.5;
x38.lo = 2.5;
x39.lo = 2.5;
x40.lo = 2.5;
x41.lo = 2.5;
x42.lo = 2.5;
x43.lo = 2.5;
x44.lo = 0.257926032525;
x45.lo = 0.299006962593291;
x46.lo = 0.346631019769593;
x47.lo = 0.401840354567059;
x48.lo = 0.465843105057112;
x49.lo = 0.540039834384121;
x50.lo = 0.626054179090777;
x51.lo = 0.725768378927107;
x52.lo = 0.841364465636933;
x53.lo = 50;
x54.lo = 50;
x55.lo = 50;
x56.lo = 50;
x57.lo = 50;
x58.lo = 50;
x59.lo = 50;
x60.lo = 50;
x61.lo = 50;
x62.lo = 5.1585206505;
x63.lo = 5.98013925186582;
x64.lo = 6.93262039539185;
x65.lo = 8.03680709134119;
x66.lo = 9.31686210114223;
x67.lo = 10.8007966876824;
x68.lo = 12.5210835818155;
x69.lo = 14.5153675785421;
x70.lo = 16.8272893127387;
x71.lo = 3.2;
x72.lo = 3.2;
x73.lo = 3.2;
x74.lo = 3.2;
x75.lo = 3.2;
x76.lo = 3.2;
x77.lo = 3.2;
x78.lo = 3.2;
x79.lo = 3.2;
x80.lo = 0.7;
x81.lo = 0.7;
x82.lo = 0.7;
x83.lo = 0.7;
x84.lo = 0.7;
x85.lo = 0.7;
x86.lo = 0.7;
x87.lo = 0.7;
x88.lo = 0.7;

* set non-default levels
x2.l = 14.6486885348509;
x3.l = 16.9818448409483;
x4.l = 19.6866124578966;
x5.l = 22.8221794332309;
x6.l = 26.4571609359673;
x7.l = 30.6711007526496;
x8.l = 35.5562119327899;
x9.l = 41.2193946739997;
x18.l = 4.926914815775;
x19.l = 5.71164461221252;
x20.l = 6.62136152055325;
x21.l = 7.67597274734501;
x22.l = 8.89855620103042;
x23.l = 10.3158655025561;
x24.l = 11.958915431079;
x25.l = 13.8636606159961;
x26.l = 16.0717823270182;
x35.l = 2.89818518575;
x36.l = 3.35979094836031;
x37.l = 3.89491854150191;
x38.l = 4.51527808667354;
x39.l = 5.23444482413554;
x40.l = 6.06815617797415;
x41.l = 7.03465613592881;
x42.l = 8.15509447999769;
x43.l = 9.45398960412836;
x53.l = 57.963703715;
x54.l = 67.1958189672061;
x55.l = 77.8983708300382;
x56.l = 90.3055617334707;
x57.l = 104.688896482711;
x58.l = 121.363123559483;
x59.l = 140.693122718576;
x60.l = 163.101889599954;
x61.l = 189.079792082567;
x71.l = 3.70967703776;
x72.l = 4.30053241390119;
x73.l = 4.98549573312245;
x74.l = 5.77955595094213;
x75.l = 6.70008937489349;
x76.l = 7.76723990780692;
x77.l = 9.00435985398888;
x78.l = 10.438520934397;
x79.l = 12.1011066932843;
x80.l = 0.81149185201;
x81.l = 0.940741465540885;
x82.l = 1.09057719162054;
x83.l = 1.26427786426859;
x84.l = 1.46564455075795;
x85.l = 1.69908372983276;
x86.l = 1.96970371806007;
x87.l = 2.28342645439935;
x88.l = 2.64711708915594;

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: 2018-09-14 Git hash: ac5a5314
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