NAG Library Manual, Mark 30.1
Interfaces:  FL   CL   CPP   AD 

NAG AD Library Introduction
Example description

 nag::ad::e04ur Tangent Over Adjoint Example Program Results
 
 *** e04us
 
 Parameters
 ----------
 
 Linear constraints.....         1       Variables..............         2
 Nonlinear constraints..         1       Subfunctions...........        44
 
 Infinite bound size....  1.00E+20       COLD start.............
 Infinite step size.....  1.00E+20       EPS (machine precision)  1.11E-16
 Step limit.............  2.00E+00       Hessian................        NO
 
 Linear feasibility.....  1.05E-08       Crash tolerance........  1.00E-02
 Nonlinear feasibility..  1.05E-08       Optimality tolerance...  3.26E-12
 Line search tolerance..  9.00E-01       Function precision.....  4.37E-15
 
 Derivative level.......         3       Monitoring file........        -1
 Verify level...........         0
 
 Major iterations limit.        50       Major print level......        10
 Minor iterations limit.        50       Minor print level......         0
 
 J'J initial Hessian....                 Reset frequency........         2
 
 Workspace provided is     IWORK(       9),  WORK(     306).
 To solve problem we need  IWORK(       9),  WORK(     306).
 
 
 Verification of the constraint gradients.
 -----------------------------------------
 
 The constraint Jacobian seems to be ok.
 
 The largest relative error was    1.89E-08  in constraint    1
 
 
 
 Verification of the objective gradients.
 ----------------------------------------
 
 The objective Jacobian seems to be ok.
 
 The largest relative error was    1.04E-08  in subfunction    3
 
 
 
  Maj  Mnr    Step Merit Function Norm Gz  Violtn Cond Hz
    0    2 0.0E+00   2.224070E-02 8.5E-02 3.6E-02 1.0E+00
    1    1 1.0E+00   1.455402E-02 1.5E-03 9.8E-03 1.0E+00
    2    1 1.0E+00   1.436491E-02 4.9E-03 7.2E-04 1.0E+00
    3    1 1.0E+00   1.427013E-02 2.9E-03 9.2E-06 1.0E+00
    4    1 1.0E+00   1.422989E-02 1.6E-04 3.6E-05 1.0E+00
    5    1 1.0E+00   1.422983E-02 5.4E-07 6.4E-08 1.0E+00
    6    1 1.0E+00   1.422983E-02 3.4E-09 9.8E-13 1.0E+00
 
 Exit from NP problem after     6 major iterations,
                                8 minor iterations.
 
 
 Varbl State     Value       Lower Bound   Upper Bound    Lagr Mult   Slack
 
 V   1    FR   0.419953      0.400000          None           .      1.9953E-02
 V   2    FR    1.28485      -4.00000          None           .       5.285
 
 
 L Con State     Value       Lower Bound   Upper Bound    Lagr Mult   Slack
 
 L   1    FR    1.70480       1.00000          None           .      0.7048
 
 
 N Con State     Value       Lower Bound   Upper Bound    Lagr Mult   Slack
 
 N   1    LL  -9.767742E-13       .            None      3.3358E-02 -9.7677E-13
 
 Exit e04us  - Optimal solution found.
 
 Final objective value =   0.1422983E-01

 Derivatives calculated: First order tangent over adjoints
 Computational mode    : algorithmic

 Solution:
 x = [4.199526524076e-01, 1.284845223872e+00]

 Sum of all Hessian entries:
 sum_ijk [d2x/druser2]_ijk = -3.252797582365e-02