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Instance launch

Formats ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)
2257.79755800 p1 ( gdx sol )
(infeas: 6e-11)
Other points (infeas > 1e-08)  
Dual Bounds
2257.79755500 (ANTIGONE)
2257.79755500 (BARON)
2257.78813500 (COUENNE)
2257.79755800 (LINDO)
2257.79733000 (SCIP)
References Bracken, Jerome and McCormick, Garth P, Chapter 7. In Bracken, Jerome and McCormick, Garth P, Selected Applications of Nonlinear Programming, John Wiley and Sons, New York, 1968, 58-82.
Source GAMS Model Library model launch
Application Launch Vehicle Design
Added to library 31 Jul 2001
Problem type NLP
#Variables 38
#Binary Variables 0
#Integer Variables 0
#Nonlinear Variables 34
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense min
Objective type nonlinear
Objective curvature indefinite
#Nonzeros in Objective 22
#Nonlinear Nonzeros in Objective 22
#Constraints 28
#Linear Constraints 16
#Quadratic Constraints 9
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 3
Operands in Gen. Nonlin. Functions div log mul vcpower
Constraints curvature indefinite
#Nonzeros in Jacobian 85
#Nonlinear Nonzeros in Jacobian 30
#Nonzeros in (Upper-Left) Hessian of Lagrangian 136
#Nonzeros in Diagonal of Hessian of Lagrangian 22
#Blocks in Hessian of Lagrangian 5
Minimal blocksize in Hessian of Lagrangian 1
Maximal blocksize in Hessian of Lagrangian 30
Average blocksize in Hessian of Lagrangian 6.8
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Minimal coefficient 7.0500e-05
Maximal coefficient 5.2728e+03
Infeasibility of initial point 5.221e+05
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
*         29       23        0        6        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         39       39        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        108       56       52        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,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;


e1..  - x1 + 0.5*x4 =E= 0;

e2..  - x2 + 0.6*x5 =E= 0;

e3..  - x3 + 0.7*x6 =E= 0;

e4..  - x4 - x5 - x6 - x7 - x8 - x9 - x10 + x11 =E= 20;

e5..  - x5 - x6 - x8 - x9 - x10 + x12 =E= 20;

e6..  - x6 - x9 - x10 + x13 =E= 20;

e7..    x17 - 5*x20 =E= 0;

e8..    x18 - 5*x21 =E= 0;

e9..    x19 - x22 =E= 0;

e10.. x26*x11 - x17 =E= 0;

e11.. x27*x12 - x18 =E= 0;

e12.. x28*x13 - x19 =E= 0;

e13.. (1 - x23)*x11 - x7 =E= 0;

e14.. (1 - x24)*x12 - x8 =E= 0;

e15.. (1 - x25)*x13 - x9 =E= 0;

e16..    12*x4 - x7 =L= 0;

e17..    10*x5 - x8 =L= 0;

e18..    7*x6 - x9 =L= 0;

e19..  - 16*x4 + x7 =L= 0;

e20..  - 12*x5 + x8 =L= 0;

e21..  - 9*x6 + x9 =L= 0;

e22.. x32*x7 - x17*x29 =E= 0;

e23.. x33*x8 - x18*x30 =E= 0;

e24.. x34*x9 - x19*x31 =E= 0;

e25.. -31.8*log(1/x23)*x32 + x35 =E= 0;

e26.. -31.8*log(1/x24)*x33 + x36 =E= 0;

e27.. -31.8*log(1/x25)*x34 + x37 =E= 0;

e28..  - x35 - x36 - x37 + x38 =E= 0;

e29.. -(5272.77*(x1**1.2781*x4**(-0.1959)*x23**2.4242*x17**0.38745*x7**(-0.9904
      ) + x2**1.2781*x5**(-0.1959)*x24**2.4242*x18**0.38745*x8**(-0.9904) + x3
      **1.2781*x6**(-0.1959)*x25**2.4242*x19**0.38745*x9**(-0.9904)) + 0.185214
      *(10.3027592771433*x1**0.3322*x23**(-1.5935)*x7**0.2362*x14**0.1079 + 
      10.3027592771433*x2**0.3322*x24**(-1.5935)*x8**0.2362*x15**0.1079 + 
      7.94328234724281*x3**0.3322*x25**(-1.5935)*x9**0.2362*x16**0.1079) + 
      160.99*(0.001*x20)**(-0.146) + 282.874*(0.001*x20)**0.648 + 160.99*(0.001
      *x21)**(-0.146) + 282.874*(0.001*x21)**0.648 + 181.806*(0.001*x22)**0.539
       + 232.57*(0.001*x22)**0.772 + 38.0226256753606*(2.509*(0.001*x20)**0.736
       + 0.0002085*x20 + 0.9744*(0.001*x20)**(-0.229)) + 38.0226256753606*(
      2.509*(0.001*x21)**0.736 + 0.0002085*x21 + 0.9744*(0.001*x21)**(-0.229))
       + 8.51138038202377*(7.05e-5*x22 - 0.000845197400305967*(0.001*x22)**(-
      1.33) + 52.5264761174087*(0.001*x22)**0.498) + 0.1637577*(1000*x10)**
      0.786 + 0.125678613298076*(1000*x10)**0.786 + 85*(0.003*x7 + 0.003*x8 + 
      0.003*x9)**0.46) + objvar =E= -850.76;

* set non-default bounds
x1.lo = 1;
x2.lo = 1;
x3.lo = 1;
x4.lo = 5;
x5.lo = 5;
x6.lo = 5;
x7.lo = 50;
x8.lo = 50;
x9.lo = 50;
x10.lo = 2.5; x10.up = 4;
x14.lo = 125; x14.up = 150;
x15.lo = 75; x15.up = 100;
x16.lo = 50; x16.up = 70;
x17.lo = 1;
x18.lo = 1;
x19.lo = 1;
x20.lo = 20;
x21.lo = 20;
x22.lo = 20;
x23.lo = 0.25; x23.up = 0.3;
x24.lo = 0.24; x24.up = 0.29;
x25.lo = 0.16; x25.up = 0.21;
x26.lo = 1.2; x26.up = 1.4;
x27.lo = 0.6; x27.up = 0.75;
x28.lo = 0.7; x28.up = 0.9;
x29.lo = 100;
x30.lo = 100;
x31.lo = 100;
x32.lo = 240; x32.up = 290;
x33.lo = 240; x33.up = 290;
x34.lo = 340; x34.up = 375;
x35.lo = 1000;
x36.lo = 1000;
x37.lo = 1000;
x38.lo = 35000; x38.up = 50000;

* set non-default levels
x4.l = 136;
x5.l = 47;
x6.l = 16;
x7.l = 2176;
x8.l = 564;
x9.l = 144;
x20.l = 746;
x21.l = 96;
x22.l = 129;
x23.l = 0.3;
x24.l = 0.29;
x25.l = 0.21;
x29.l = 155;
x30.l = 314;
x31.l = 403;
x38.l = 38632;

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: 2022-08-11 Git hash: f176bd52
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