nag_opt_nlp_sparse (e04ugc) Example Program Results
Optional parameter setting for e04ugc.
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Option file: e04ugce.opt
minor_iter_lim = 20
iter_lim = 30
Parameters to e04ugc
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Frequencies.
fcheck.................. 60 expand_freq............ 10000
factor_freq............. 50
QP subproblems.
scale_tol............... 9.00e-01 minor_feas_tol......... 1.05e-08
scale_opt............... 1 minor_opt_tol.......... 1.05e-08
part_price.............. 1 crash_tol.............. 1.00e-01
pivot_tol............... 2.04e-11 minor_print_level..... Nag_NoPrint
crash.................. Nag_NoCrash elastic_wt............. 1.00e+02
Derivatives.
obj_deriv............... Nag_TRUE con_deriv.............. Nag_TRUE
verify_grad........ Nag_SimpleCheck print_deriv........... Nag_D_Print
Start obj check at col.. 1 Stop obj check at col.. 4
Start con check at col.. 1 Stop con check at col.. 2
The SQP method.
direction............. Nag_Minimize
Nonlinear objective vars 4 major_opt_tol.......... 1.05e-08
f_prec.................. 1.72e-13 inf_step............... 1.00e+20
max_sb.................. 4 f_diff_int............. 4.15e-07
unbounded_obj........... 1.00e+15 c_diff_int............. 5.56e-05
major_step_lim.......... 2.00e+00 deriv_linesearch....... Nag_TRUE
print_level.......... Nag_Soln_Iter major_iter_lim......... 100
linesearch_tol.......... 9.00e-01 minor_iter_lim......... 20
inf_bound............... 1.00e+20 iter_lim............... 30
Hessian approximation.
hess_storage....... Nag_HessianFull hess_update............ 20
hess_freq............... 99999999
Nonlinear constraints.
Nonlinear constraints... 3 major_feas_tol......... 1.05e-08
Nonlinear Jacobian vars. 2 violation_limit........ 1.00e+01
Miscellaneous.
Variables............... 4 Linear constraints..... 3
Nonlinear variables..... 4 Linear variables....... 0
lu_factor_tol........... 5.00e+00 lu_sing_tol............ 2.04e-11
lu_update_tol........... 5.00e+00 lu_den_tol............. 6.00e-01
eps (machine precision). 1.11e-16
start................... Nag_Cold feas_exit.............. Nag_FALSE
Names.................... supplied print_80ch............. Nag_TRUE
outfile................. stdout
Memory allocation.
nz_coef................. 5.00e+00 Initial sizes of work arrays.
state................... Nag Integers............... 1628
lambda.................. Nag Reals.................. 1258
XXX Scale option reduced from 1 to 0.
XXX Feasible linear rows.
XXX Norm(x-x0) minimized. Sum of infeasibilities = 0.00e+00.
confun sets 6 out of 6 constraint gradients.
objfun sets 4 out of 4 objective gradients.
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Verification of constraint gradients returned by subroutine confun
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Cheap test on confun...
The Jacobian seems to be OK.
The largest discrepancy was 4.41e-08 in constraint 2.
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Verification of objective gradients returned by subroutine objfun
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Cheap test on objfun...
The objective gradients seem to be OK.
Gradient projected in two directions 0.00000000000e+00 0.00000000000e+00
Difference approximations 1.74111992322e-19 4.48742248252e-21
XXX All-slack basis B = I selected.
XXX Large multipliers.
Elastic mode started with weight = 2.0e+02.
Maj Mnr Step Merit Function Feasibl Optimal Cond Hz PD
0 8 0.0e+00 3.199952e+05 1.7e+00 8.0e-01 1.0e+00 FF R i
1 4 1.0e+00 2.419951e+05 7.7e-01 3.7e+01 1.0e+00 FF s
2 1 1.0e+00 5.172188e+03 2.9e-02 1.9e+00 1.0e+00 FF
3 1 3.8e-01 5.038588e+03 1.8e-02 4.6e+00 1.2e+02 FF
4 1 3.6e-01 5.120830e+03 1.2e-02 2.0e+00 1.6e+02 FF
5 1 1.0e+00 5.126491e+03 1.0e-04 3.6e-02 1.7e+02 FF
6 1 3.1e-01 5.126498e+03 7.1e-05 3.1e-02 1.1e+02 FF
7 1 1.0e+00 5.126498e+03 4.3e-09 6.5e-04 1.1e+02 TF
8 1 1.0e+00 5.126498e+03 4.5e-13 4.8e-05 1.1e+02 TF
9 0 1.0e+00 5.126498e+03 1.2e-15 3.5e-13 1.1e+02 TT
Exit from NP problem after 9 major iterations,
19 minor iterations.
Variable State Value Lower Bound Upper Bound Lagr Mult Residual
Varble 1 BS 1.188764e-01 -5.50000e-01 5.50000e-01 -1.8190e-12 4.3112e-01
Varble 2 BS -3.962336e-01 -5.50000e-01 5.50000e-01 1.6371e-11 1.5377e-01
Varble 3 BS 6.799453e+02 0.00000e+00 1.20000e+03 -2.9310e-14 5.2005e+02
Varble 4 SBS 1.026067e+03 0.00000e+00 1.20000e+03 -6.6613e-14 1.7393e+02
Constrnt State Value Lower Bound Upper Bound Lagr Mult Residual
NlnCon 1 EQ -8.948000e+02 -8.94800e+02 -8.94800e+02 -4.3870e+00 3.4106e-12
NlnCon 2 EQ -8.948000e+02 -8.94800e+02 -8.94800e+02 -4.1056e+00 4.5475e-13
NlnCon 3 EQ -1.294800e+03 -1.29480e+03 -1.29480e+03 -5.4633e+00 3.4106e-12
LinCon 1 BS 2.773572e-01 -5.50000e-0 None 25 0.0000e+00 8.2736e-01
LinCon 2 BS -2.773572e-01 -5.50000e-0 None 25 0.0000e+00 2.7264e-01
Free Row BS 4.091970e+03 None None 25 -1.0000e+00 4.0920e+03
Exit e04ugc - Optimal solution found.
Final objective value = 5126.498
A run of the same example with a warm start:
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Parameters to e04ugc
--------------------
Frequencies.
fcheck.................. 60 expand_freq............ 10000
factor_freq............. 50
QP subproblems.
scale_tol............... 9.00e-01 minor_feas_tol......... 1.05e-08
scale_opt............... 1 minor_opt_tol.......... 1.05e-08
part_price.............. 1 crash_tol.............. 1.00e-01
pivot_tol............... 2.04e-11 minor_print_level..... Nag_NoPrint
crash.................. Nag_NoCrash elastic_wt............. 1.00e+02
Derivatives.
obj_deriv............... Nag_TRUE con_deriv.............. Nag_TRUE
verify_grad........ Nag_SimpleCheck print_deriv......... Nag_D_NoPrint
Start obj check at col.. 1 Stop obj check at col.. 4
Start con check at col.. 1 Stop con check at col.. 2
The SQP method.
direction............. Nag_Minimize
Nonlinear objective vars 4 major_opt_tol.......... 1.05e-08
f_prec.................. 1.72e-13 inf_step............... 1.00e+20
max_sb.................. 4 f_diff_int............. 4.15e-07
unbounded_obj........... 1.00e+15 c_diff_int............. 5.56e-05
major_step_lim.......... 2.00e+00 deriv_linesearch....... Nag_TRUE
print_level............... Nag_Iter major_iter_lim......... 100
linesearch_tol.......... 9.00e-01 minor_iter_lim......... 20
inf_bound............... 1.00e+20 iter_lim............... 30
Hessian approximation.
hess_storage....... Nag_HessianFull hess_update............ 20
hess_freq............... 99999999
Nonlinear constraints.
Nonlinear constraints... 3 major_feas_tol......... 1.05e-08
Nonlinear Jacobian vars. 2 violation_limit........ 1.00e+01
Miscellaneous.
Variables............... 4 Linear constraints..... 3
Nonlinear variables..... 4 Linear variables....... 0
lu_factor_tol........... 5.00e+00 lu_sing_tol............ 2.04e-11
lu_update_tol........... 5.00e+00 lu_den_tol............. 6.00e-01
eps (machine precision). 1.11e-16
start................... Nag_Warm feas_exit.............. Nag_FALSE
Names.................... supplied print_80ch............. Nag_TRUE
outfile................. stdout
Memory allocation.
nz_coef................. 5.00e+00 Initial sizes of work arrays.
state................... Nag Integers............... 1628
lambda.................. Nag Reals.................. 1258
XXX Scale option reduced from 1 to 0.
XXX Feasible linear rows.
XXX Norm(x-x0) minimized. Sum of infeasibilities = 0.00e+00.
XXX All-slack basis B = I selected.
Maj Mnr Step Merit Function Feasibl Optimal Cond Hz PD
0 1 0.0e+00 5.128197e+03 1.3e-01 1.1e+00 1.7e+00 FF R
1 1 1.0e+00 4.883655e+03 3.5e-03 5.7e-01 2.0e+02 FF S
2 1 1.8e-01 5.126320e+03 2.8e-03 3.7e+00 1.9e+02 FF
3 1 2.8e-01 5.126417e+03 2.0e-03 1.1e+00 1.9e+02 FF
4 1 1.0e+00 5.126499e+03 3.2e-06 1.9e-01 2.0e+02 FF
5 1 1.0e+00 5.126498e+03 1.1e-08 4.2e-02 1.1e+02 FF
6 1 1.0e+00 5.126498e+03 2.2e-09 1.2e-06 1.1e+02 TF
7 1 1.0e+00 5.126498e+03 4.0e-17 2.7e-10 1.1e+02 TT
Exit from NP problem after 7 major iterations,
8 minor iterations.
Exit e04ugc - Optimal solution found.
Final objective value = 5126.498