tp054v1.apm

Model tp054v1
  ! Source version 1

  ! Exact formulation of #54.
  ! Using IEEE 754 double precision,
  ! we might be in some trouble here due to
  ! the fact that the variables, x[i], move
  ! in different orders of magnitude.
  ! R.J.Vanderbei and J.D.Hedengren used the y[i]
  ! instead of the x[i] here as the variables,
  ! and J.D.Hedengren additionally
  ! replaced -exp(-(...)/2) by (...),
  ! simplifying the objective function once more.

  Variables
    x[1] =     6000    , >=   0, <=     20000
    x[2] =        1.5  , >= -10, <=        10
    x[3] =  4000000    , >=   0, <=  10000000
    x[4] =        2    , >=   0, <=        20
    x[5] =        0.003, >=  -1, <=         1
    x[6] = 50000000    , >=   0, <= 200000000
    obj
  End Variables

  Intermediates
    y[1] = (x[1] - 10000)/8000
    y[2] = (x[2] - 1)/1
    y[3] = (x[3] - 2000000)/7000000
    y[4] = (x[4] - 10)/50
    y[5] = (x[5] - 1/1000)*20
    y[6] = (x[6] - 100000000)/500000000
    h1 = (y[1]^2 + y[1]*y[2]*2/5 + y[2]^2)*25/24
    h2 = y[3]^2 + y[4]^2 + y[5]^2 + y[6]^2
    mf = -exp(-(h1 + h2)/2)
  End Intermediates

  Equations
    x[1] + 4000*x[2] - 17600 = 0

    obj = mf

    ! best known objective = -exp(-27/280) = -0.9080747577659853
    ! begin of best known solution
    ! x[1] = 91600/7 = 13085.71428571429
    ! x[2] = 79/70 = 1.128571428571429
    ! x[3] = 2000000
    ! x[4] = 10
    ! x[5] = 1/1000 = 0.001
    ! x[6] = 100000000
    ! end of best known solution
  End Equations
End Model