NAG Library Manual, Mark 30
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NAG CL Interface Introduction
Example description

nag_opt_qp_dense_solve (e04nfc) Example Program Results

Optional parameter setting for e04nfc.
--------------------------------------

Option file: e04nfce.opt

fmax_iter set to 30
max_iter set to 50

Parameters to e04nfc
--------------------

Linear constraints............   7    Number of variables...........   7

prob....................   Nag_QP2    start...................  Nag_Cold
ftol....................  1.05e-08    reset_ftol..............         5
rank_tol................  1.11e-14    crash_tol...............  1.00e-02
fcheck..................        50    max_df..................         7
inf_bound...............  1.00e+21    inf_step................  1.00e+21
fmax_iter...............        30    max_iter................        50
hrows...................         7    machine precision.......  1.11e-16
optim_tol...............  1.72e-13    min_infeas.............. Nag_FALSE
print_level......... Nag_Soln_Iter
outfile.................    stdout

Memory allocation:
state...................       Nag
ax......................       Nag    lambda..................       Nag

Results from e04nfc:
-------------------

  Itn Jdel  Jadd   Step    Ninf  Sinf/Obj    Bnd  Lin  Nart  Nrz  Norm Gz

   0   0     0    0.0e+00   3   1.0380e-01    3    4    0     0   0.00e+00
   1   9 U  13 L  4.1e-02   1   3.0000e-02    3    4    0     0   0.00e+00
   2  12 U   4 L  4.2e-02   0   0.0000e+00    4    3    0     0   0.00e+00
(User-supplied callback qphess1, first invocation.)

 Itn 2  -- Feasible point found.
   2   0     0    0.0e+00   0   4.5800e-02    4    3    0     0   0.00e+00
   3   5 L  14 L  1.3e-01   0   4.1616e-02    3    4    0     0   0.00e+00
   4  11 U   0    1.0e+00   0   3.9362e-02    3    3    0     1   4.16e-17
   5   3 L  10 U  4.1e-01   0   3.7589e-02    2    4    0     1   1.19e-02
   6   0     0    1.0e+00   0   3.7554e-02    2    4    0     1   1.04e-17
   7   4 L   0    1.0e+00   0   3.7032e-02    1    4    0     2   3.80e-17

Final solution:

  Varbl State    Value      Lower Bound  Upper Bound    Lagr Mult    Residual

 V   1    LL  -1.00000e-02  -1.0000e-02   1.0000e-02    4.700e-01   0.000e+00
 V   2    FR  -6.98646e-02  -1.0000e-01   1.5000e-01    0.000e+00   3.014e-02
 V   3    FR   1.82592e-02  -1.0000e-02   3.0000e-02    0.000e+00   1.174e-02
 V   4    FR  -2.42608e-02  -4.0000e-02   2.0000e-02    0.000e+00   1.574e-02
 V   5    FR  -6.20056e-02  -1.0000e-01   5.0000e-02    0.000e+00   3.799e-02
 V   6    FR   1.38054e-02  -1.0000e-02   None       0.000e+00   2.381e-02
 V   7    FR   4.06650e-03  -1.0000e-02   None       0.000e+00   1.407e-02

   LCon  State    Value     Lower Bound  Upper Bound    Lagr Mult    Residual

 L   1    EQ  -1.30000e-01  -1.3000e-01  -1.3000e-01   -1.908e+00   2.776e-17
 L   2    FR  -5.87990e-03     None      -4.9000e-03    0.000e+00   9.799e-04
 L   3    UL  -6.40000e-03     None      -6.4000e-03   -3.144e-01   0.000e+00
 L   4    FR  -4.53732e-03     None      -3.7000e-03    0.000e+00   8.373e-04
 L   5    FR  -2.91600e-03     None      -1.2000e-03    0.000e+00   1.716e-03
 L   6    LL  -9.92000e-02  -9.9200e-02   None       1.955e+00   1.388e-17
 L   7    LL  -3.00000e-03  -3.0000e-03   2.0000e-03    1.972e+00  -4.337e-19

Exit after 7 iterations.

Optimal QP solution found.

Final QP objective value =   3.7031646e-02


A run of the same example with a warm start:

Parameters to e04nfc
--------------------

Linear constraints............   7    Number of variables...........   7

prob....................   Nag_QP2    start...................  Nag_Warm
ftol....................  1.05e-08    reset_ftol..............         5
rank_tol................  1.11e-14    crash_tol...............  1.00e-02
fcheck..................        50    max_df..................         7
inf_bound...............  1.00e+21    inf_step................  1.00e+21
fmax_iter...............        30    max_iter................        50
hrows...................         7    machine precision.......  1.11e-16
optim_tol...............  1.72e-13    min_infeas.............. Nag_FALSE
print_level.........      Nag_Soln
outfile.................    stdout

Memory allocation:
state...................       Nag
ax......................       Nag    lambda..................       Nag
(User-supplied callback qphess2, first invocation.)

Final solution:

  Varbl State    Value      Lower Bound  Upper Bound    Lagr Mult    Residual

 V   1    LL  -1.00000e-02  -1.0000e-02   1.0000e-02    4.700e-01   0.000e+00
 V   2    FR  -6.98646e-02  -1.0000e-01   1.5000e-01    0.000e+00   3.014e-02
 V   3    FR   1.82592e-02  -1.0000e-02   3.0000e-02    0.000e+00   1.174e-02
 V   4    FR  -2.42608e-02  -4.0000e-02   2.0000e-02    0.000e+00   1.574e-02
 V   5    FR  -6.20056e-02  -1.0000e-01   5.0000e-02    0.000e+00   3.799e-02
 V   6    FR   1.38054e-02  -1.0000e-02   None       0.000e+00   2.381e-02
 V   7    FR   4.06650e-03  -1.0000e-02   None       0.000e+00   1.407e-02

   LCon  State    Value     Lower Bound  Upper Bound    Lagr Mult    Residual

 L   1    EQ  -1.30000e-01  -1.3000e-01  -1.3000e-01   -1.908e+00   0.000e+00
 L   2    FR  -5.87990e-03     None      -4.9000e-03    0.000e+00   9.799e-04
 L   3    UL  -6.40000e-03     None      -6.4000e-03   -3.144e-01   0.000e+00
 L   4    FR  -4.53732e-03     None      -3.7000e-03    0.000e+00   8.373e-04
 L   5    FR  -2.91600e-03     None      -1.2000e-03    0.000e+00   1.716e-03
 L   6    LL  -9.92000e-02  -9.9200e-02   None       1.955e+00   0.000e+00
 L   7    LL  -3.00000e-03  -3.0000e-03   2.0000e-03    1.972e+00  -1.735e-18

Exit after 0 iterations.

Optimal QP solution found.

Final QP objective value =   3.7031646e-02