NAG Library Manual, Mark 28.3
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NAG CL Interface Introduction
Example description

nag_opt_bounds_deriv (e04kbc) Example Program Results

Optional parameter setting for e04kbc.
--------------------------------------

Option file: e04kbce.opt

print_level set to Nag_Soln_Iter_Full
max_iter set to 40
step_max set to 4.00e+00
f_est set to 0.00e+00

Parameters to e04kbc
--------------------

Number of variables...........   4

optim_tol...............  1.05e-07    linesearch_tol..........  9.00e-01
f_est...................  0.00e+00
step_max................  4.00e+00    max_iter................        40
init_state.......... Nag_Init_None    local_search............      Nag_TRUE
minlin.............. Nag_Lin_Deriv    deriv_check.............      Nag_TRUE
print_level.... Nag_Soln_Iter_Full    machine precision.......  1.11e-16
outfile.................    stdout

Memory allocation:
state...................       Nag
hesl....................       Nag    hesd...................        Nag

Results from e04kbc:
-------------------

Iteration results:

  Itn  Nfun  Objective    Norm g    Norm x  Norm(x(k-1)-x(k))  Step    Cond H
   0     0   1.7284e+02   2.9e+02   3.3e+00                            1.0e+00

 Variable         x                g          Status
    1         3.0000e+00       2.6236e+02    Upper Bound
    2        -9.0000e-01      -1.2624e+02    Free
    3         1.3000e-01       2.7872e+00    Free
    4         1.1000e+00      -2.6466e+02    Free

  Itn  Nfun  Objective    Norm g    Norm x  Norm(x(k-1)-x(k))  Step    Cond H
   1     1   2.6813e+01   2.7e+01   3.7e+00     1.2e+00      4.0e-03   3.4e+01

 Variable         x                g          Status
    1         3.0000e+00       2.1529e+01    Upper Bound
    2        -3.9251e-01      -1.9503e+01    Free
    3         1.1880e-01      -1.8450e+01    Free
    4         2.1639e+00      -2.9276e+00    Free

  Itn  Nfun  Objective    Norm g    Norm x  Norm(x(k-1)-x(k))  Step    Cond H
   2     3   2.3453e+01   2.0e+01   3.7e+00     2.6e-01      1.0e-02   4.2e+01

 Variable         x                g          Status
    1         3.0000e+00       2.9429e+01    Upper Bound
    2        -2.2652e-01       1.2204e+01    Free
    3         3.1377e-01      -1.3004e+01    Free
    4         2.1125e+00      -9.9713e+00    Free

  Itn  Nfun  Objective    Norm g    Norm x  Norm(x(k-1)-x(k))  Step    Cond H
   3     6   2.1599e+01   2.8e+01   3.7e+00     2.2e-01      8.7e-03   2.3e+02

 Variable         x                g          Status
    1         3.0000e+00       2.6022e+01    Free
    2        -2.5718e-01      -6.5438e-01    Free
    3         5.3184e-01       2.3232e+00    Free
    4         2.1431e+00      -9.0525e+00    Free

  Itn  Nfun  Objective    Norm g    Norm x  Norm(x(k-1)-x(k))  Step    Cond H
   4     8   1.6189e+01   2.3e+01   3.1e+00     8.0e-01      3.1e-02   8.9e+00

 Variable         x                g          Status
    1         2.1985e+00      -7.4626e-01    Free
    2        -2.5748e-01      -1.6715e+01    Free
    3         5.3101e-01       2.2448e+00    Free
    4         2.1444e+00       1.6128e+01    Free

  Itn  Nfun  Objective    Norm g    Norm x  Norm(x(k-1)-x(k))  Step    Cond H
   5     9   1.4024e+01   1.5e+01   3.0e+00     1.7e-01      1.0e+00   1.8e+01

 Variable         x                g          Status
    1         2.0816e+00       7.7589e-01    Free
    2        -1.6942e-01       8.3975e-01    Free
    3         5.1518e-01      -1.5466e+00    Free
    4         2.0515e+00       1.5362e+01    Free

  Itn  Nfun  Objective    Norm g    Norm x  Norm(x(k-1)-x(k))  Step    Cond H
   6    10   1.1240e+01   2.1e+01   2.6e+00     3.8e-01      1.0e+00   5.4e+01

 Variable         x                g          Status
    1         1.7877e+00       2.1366e+00    Free
    2        -7.1798e-02       1.5908e+01    Free
    3         5.1964e-01      -2.1209e+00    Free
    4         1.8290e+00       1.3096e+01    Free

  Itn  Nfun  Objective    Norm g    Norm x  Norm(x(k-1)-x(k))  Step    Cond H
   7    11   7.9843e+00   1.1e+01   2.1e+00     5.4e-01      6.2e-01   3.9e+00

 Variable         x                g          Status
    1         1.3605e+00       2.5858e+00    Free
    2         0.0000e+00       2.3422e+01    Upper Bound
    3         4.9104e-01      -2.6186e+00    Free
    4         1.5106e+00       1.0331e+01    Free

  Itn  Nfun  Objective    Norm g    Norm x  Norm(x(k-1)-x(k))  Step    Cond H
   8    12   5.3035e+00   9.3e+00   1.7e+00     3.7e-01      1.0e+00   1.1e+01

 Variable         x                g          Status
    1         1.0732e+00       1.7792e+00    Free
    2         0.0000e+00       1.8627e+01    Upper Bound
    3         4.4590e-01      -2.6928e+00    Free
    4         1.2826e+00       8.7338e+00    Free

  Itn  Nfun  Objective    Norm g    Norm x  Norm(x(k-1)-x(k))  Step    Cond H
   9    13   4.6913e+00   1.9e+01   1.6e+00     9.5e-02      6.6e-02   7.3e+01

 Variable         x                g          Status
    1         1.0000e+00       1.5613e+00    Lower Bound
    2         0.0000e+00       1.7336e+01    Free
    3         4.3666e-01      -2.5266e+00    Free
    4         1.2222e+00       8.2939e+00    Free

  Itn  Nfun  Objective    Norm g    Norm x  Norm(x(k-1)-x(k))  Step    Cond H
  10    15   3.9688e+00   8.3e+00   1.6e+00     8.3e-02      4.8e-03   3.9e+00

 Variable         x                g          Status
    1         1.0000e+00      -9.4589e-02    Lower Bound
    2        -8.3009e-02      -1.0146e-01    Free
    3         4.3672e-01      -8.4789e-01    Free
    4         1.2215e+00       8.2818e+00    Free

  Itn  Nfun  Objective    Norm g    Norm x  Norm(x(k-1)-x(k))  Step    Cond H
  11    16   2.8304e+00   6.4e+00   1.5e+00     1.6e-01      1.0e+00   1.9e+01

 Variable         x                g          Status
    1         1.0000e+00       3.1074e-01    Lower Bound
    2        -8.3930e-02      -3.6206e-02    Free
    3         4.2460e-01       1.0297e-01    Free
    4         1.0643e+00       6.4079e+00    Free

  Itn  Nfun  Objective    Norm g    Norm x  Norm(x(k-1)-x(k))  Step    Cond H
  12    17   2.4344e+00   2.4e-01   1.5e+00     6.5e-02      1.1e-01   2.6e+00

 Variable         x                g          Status
    1         1.0000e+00       3.0156e-01    Lower Bound
    2        -8.4922e-02      -3.4052e-02    Free
    3         4.1431e-01       2.4239e-01    Free
    4         1.0000e+00       5.8569e+00    Lower Bound

  Itn  Nfun  Objective    Norm g    Norm x  Norm(x(k-1)-x(k))  Step    Cond H
  13    18   2.4339e+00   8.7e-02   1.5e+00     3.2e-03      1.0e+00   4.1e+00

 Variable         x                g          Status
    1         1.0000e+00       2.9879e-01    Lower Bound
    2        -8.5060e-02      -7.5964e-05    Free
    3         4.1114e-01       8.7488e-02    Free
    4         1.0000e+00       5.8886e+00    Lower Bound

  Itn  Nfun  Objective    Norm g    Norm x  Norm(x(k-1)-x(k))  Step    Cond H
  14    19   2.4338e+00   7.8e-04   1.5e+00     1.8e-03      1.0e+00   4.1e+00

 Variable         x                g          Status
    1         1.0000e+00       2.9535e-01    Lower Bound
    2        -8.5233e-02      -2.7717e-04    Free
    3         4.0932e-01       7.2996e-04    Free
    4         1.0000e+00       5.9068e+00    Lower Bound

  Itn  Nfun  Objective    Norm g    Norm x  Norm(x(k-1)-x(k))  Step    Cond H
  15    20   2.4338e+00   3.5e-06   1.5e+00     1.5e-05      1.0e+00   4.1e+00

 Variable         x                g          Status
    1         1.0000e+00       2.9535e-01    Lower Bound
    2        -8.5233e-02      -2.5483e-06    Free
    3         4.0930e-01       2.3869e-06    Free
    4         1.0000e+00       5.9070e+00    Lower Bound

  Itn  Nfun  Objective    Norm g    Norm x  Norm(x(k-1)-x(k))  Step    Cond H
  16    21   2.4338e+00   8.2e-09   1.5e+00     4.6e-08      1.0e+00   4.1e+00

 Variable         x                g          Status
    1         1.0000e+00       2.9535e-01    Lower Bound
    2        -8.5233e-02      -8.1823e-09    Free
    3         4.0930e-01       1.0494e-10    Free
    4         1.0000e+00       5.9070e+00    Lower Bound

  Itn  Nfun  Objective    Norm g    Norm x  Norm(x(k-1)-x(k))  Step    Cond H
  17    22   2.4338e+00   8.2e-09   1.5e+00     4.2e-11      1.0e+00   1.0e+00

 Variable         x                g          Status
    1         1.0000e+00       2.9535e-01    Lower Bound
    2        -8.5233e-02      -8.1823e-09    Free
    3         4.0930e-01       1.0494e-10    Free
    4         1.0000e+00       5.9070e+00    Lower Bound

  Itn  Nfun  Objective    Norm g    Norm x  Norm(x(k-1)-x(k))  Step    Cond H
  18    23   2.4338e+00   8.2e-09   1.5e+00     4.2e-11      1.0e+00   1.0e+00

 Variable         x                g          Status
    1         1.0000e+00       2.9535e-01    Lower Bound
    2        -8.5233e-02      -8.1823e-09    Free
    3         4.0930e-01       1.0494e-10    Free
    4         1.0000e+00       5.9070e+00    Lower Bound

Local search performed.

Final solution:

  Itn  Nfun  Objective    Norm g    Norm x  Norm(x(k-1)-x(k))  Step    Cond H
  18    27   2.4338e+00   8.2e-09   1.5e+00     8.2e-09      1.0e+00   1.0e+00

 Variable         x                g          Status
    1         1.0000e+00       2.9535e-01    Lower Bound
    2        -8.5233e-02      -8.1823e-09    Free
    3         4.0930e-01       1.0494e-10    Free
    4         1.0000e+00       5.9070e+00    Lower Bound
Error/Warning from nag_opt_bounds_deriv (e04kbc).
NW_COND_MIN:
  The conditions for a minimum have not all been satisfied but a lower
  point could not be found.