nag_opt_sparse_convex_qp (e04nkc) Example Program Results

Parameters to e04nkc
--------------------

Problem type............ sparse QP    Number of variables.....         7
Linear constraints......         8    Hessian columns.........         7    

prob_name...............          
obj_name................              rhs_name................          
range_name..............              bnd_name................          
crnames.................  supplied

minimize................  Nag_TRUE    start...................  Nag_Cold
ftol....................  1.00e-06    reset_ftol..............     10000
fcheck..................        60    factor_freq.............       100
scale.............. Nag_ExtraScale    scale_tol...............  9.00e-01
optim_tol...............  1.00e-06    max_iter................        75
crash.............. Nag_CrashTwice    crash_tol...............  1.00e-01
partial_price...........        10    pivot_tol...............  2.05e-11
max_sb..................         7    
inf_bound...............  1.00e+20    inf_step................  1.00e+20
lu_factor_tol...........  1.00e+02    lu_update_tol...........  1.00e+01
lu_sing_tol.............  2.05e-11    machine precision.......  1.11e-16
print_level......... Nag_Soln_Iter
outfile.................    stdout

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

   Itn      Step   Ninf   Sinf/Objective   Norm rg
Itn 0 -- Infeasible
     0   0.0e+00      1     1.152891e+03   0.0e+00
     1   4.3e+02      0     0.000000e+00   0.0e+00
Itn 1 -- Feasible point found (for 1 equality constraints).
     1   0.0e+00      0     0.000000e+00   0.0e+00
     1   0.0e+00      0     1.460000e+06   0.0e+00
Itn 1 -- Feasible QP solution.
     2   8.7e-02      0     9.409959e+05   0.0e+00
     3   5.3e-01      0    -1.056552e+06   0.0e+00
     4   1.0e+00      0    -1.462190e+06   4.1e-12
     5   1.0e+00      0    -1.698092e+06   1.8e-12
     6   4.6e-02      0    -1.764906e+06   7.0e+02
     7   1.0e+00      0    -1.811946e+06   9.1e-13
     8   1.7e-02      0    -1.847325e+06   1.7e+02
     9   1.0e+00      0    -1.847785e+06   5.2e-12

Variable State         Value   Lower Bound  Upper Bound   Lagr Mult    Residual
COLUMN 1    LL   0.00000e+00    0.0000e+00   2.0000e+02   2.361e+03   0.000e+00
COLUMN 2    BS   3.49399e+02    0.0000e+00   2.5000e+03  -1.062e-12   3.494e+02
COLUMN 3   SBS   6.48853e+02    4.0000e+02   8.0000e+02  -4.395e-12   1.511e+02
COLUMN 4   SBS   1.72847e+02    1.0000e+02   7.0000e+02  -2.274e-12   7.285e+01
COLUMN 5    BS   4.07521e+02    0.0000e+00   1.5000e+03  -2.067e-12   4.075e+02
COLUMN 6    BS   2.71356e+02    0.0000e+00         None   7.455e-13   2.714e+02
COLUMN 7    BS   1.50023e+02    0.0000e+00         None   4.710e-13   1.500e+02

Constrnt State         Value   Lower Bound  Upper Bound   Lagr Mult    Residual
OBJECTIV    EQ   2.00000e+03    2.0000e+03   2.0000e+03  -1.290e+04  -0.000e+00
ROW    1    BS   4.92316e+01          None   6.0000e+01  -1.349e-11  -1.077e+01
ROW    2    UL   1.00000e+02          None   1.0000e+02  -2.325e+03   0.000e+00
ROW    3    BS   3.20719e+01          None   4.0000e+01   0.000e+00  -7.928e+00
ROW    4    BS   1.45572e+01          None   3.0000e+01   0.000e+00  -1.544e+01
ROW    5    LL   1.50000e+03    1.5000e+03         None   1.445e+04  -0.000e+00
ROW    6    LL   2.50000e+02    2.5000e+02   3.0000e+02   1.458e+04  -0.000e+00
ROW    7    BS  -2.98869e+06          None         None  -1.000e+00  -2.989e+06

Exit after 9 iterations.

Optimal QP solution found.

Final QP objective value =  -1.8477847e+06


Perturb the problem and re-solve with warm start.

Parameters to e04nkc
--------------------

Problem type............ sparse QP    Number of variables.....         7
Linear constraints......         8    Hessian columns.........         7    

prob_name...............          
obj_name................              rhs_name................          
range_name..............              bnd_name................          
crnames.................  supplied

minimize................  Nag_TRUE    start...................  Nag_Warm
ftol....................  1.00e-06    reset_ftol..............     10000
fcheck..................        60    factor_freq.............       100
scale.............. Nag_ExtraScale    scale_tol...............  9.00e-01
optim_tol...............  1.00e-06    max_iter................        75
crash.............. Nag_CrashTwice    crash_tol...............  1.00e-01
partial_price...........        10    pivot_tol...............  2.05e-11
max_sb..................         7    
inf_bound...............  1.00e+20    inf_step................  1.00e+20
lu_factor_tol...........  1.00e+02    lu_update_tol...........  1.00e+01
lu_sing_tol.............  2.05e-11    machine precision.......  1.11e-16
print_level.............  Nag_Soln
outfile.................    stdout

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

Variable State         Value   Lower Bound  Upper Bound   Lagr Mult    Residual
COLUMN 1    LL   0.00000e+00    0.0000e+00   2.0000e+02   2.360e+03   0.000e+00
COLUMN 2   SBS   3.49529e+02    0.0000e+00   2.5000e+03  -1.769e-12   3.495e+02
COLUMN 3    BS   6.48762e+02    4.0000e+02   8.0000e+02  -7.644e-13   1.512e+02
COLUMN 4   SBS   1.72618e+02    1.0000e+02   7.0000e+02  -1.624e-12   7.262e+01
COLUMN 5    BS   4.07596e+02    0.0000e+00   1.5000e+03  -3.446e-13   4.076e+02
COLUMN 6    BS   2.71446e+02    0.0000e+00         None  -5.964e-13   2.714e+02
COLUMN 7    BS   1.50048e+02    0.0000e+00         None   7.850e-13   1.500e+02

Constrnt State         Value   Lower Bound  Upper Bound   Lagr Mult    Residual
OBJECTIV    EQ   2.00000e+03    2.0000e+03   2.0000e+03  -1.290e+04  -0.000e+00
ROW    1    BS   4.92290e+01          None   6.0000e+01   0.000e+00  -1.077e+01
ROW    2    UL   1.00000e+02          None   1.0000e+02  -2.325e+03   0.000e+00
ROW    3    BS   3.20731e+01          None   4.0000e+01   0.000e+00  -7.927e+00
ROW    4    BS   1.45618e+01          None   3.0000e+01   0.000e+00  -1.544e+01
ROW    5    LL   1.50000e+03    1.5000e+03         None   1.446e+04  -0.000e+00
ROW    6    LL   2.50000e+02    2.5000e+02   3.0000e+02   1.458e+04  -0.000e+00
ROW    7    BS  -2.98841e+06          None         None  -1.000e+00  -2.988e+06

Exit after 1 iterations.

Optimal QP solution found.

Final QP objective value =  -1.8466439e+06