NAG Library Manual, Mark 28.7
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nag::ad::e04ur Tangent over Tangent 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).

-----------------------------------------

The constraint Jacobian seems to be ok.

The largest relative error was    1.89E-08  in constraint    1

----------------------------------------

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 tangents
Computational mode    : algorithmic

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

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