NAG Library Manual, Mark 30.2
Interfaces:  FL   CL   CPP   AD 

NAG FL Interface Introduction
Example description

 E04WEF Example Program Results
 
 
 OPTIONS file
 ------------
 
      Begin example options file
      * Comment lines like this begin with an asterisk.
      * Switch off output of timing information:
      Timing level 0
      * Allow elastic variables:
      Elastic mode 1
      * Set the feasibility tolerance:
      Feasibility tolerance 1.0D-4
      End
 
 E04WEZ EXIT 100 -- finished successfully
 E04WEZ INFO 101 -- OPTIONS file read
 
 Option 'Elastic mode' has the value   1.
 Option 'Feasibility tolerance' has the value   1.00000E-04.
 
 Parameters
 ==========
 
 Files
 -----
 Solution file..........         0       Old basis file ........         0       (Print file)...........         6
 Insert file............         0       New basis file ........         0       (Summary file).........         0
 Punch file.............         0       Backup basis file......         0
 Load file..............         0       Dump file..............         0
 
 Frequencies
 -----------
 Print frequency........       100       Check frequency........        60       Save new basis map.....       100
 Summary frequency......       100       Factorization frequency        50       Expand frequency.......     10000
 
 QP subproblems
 --------------
 QPsolver Cholesky......
 Scale tolerance........     0.900       Minor feasibility tol..  1.00E-04       Iteration limit........     10000
 Scale option...........         0       Minor optimality  tol..  1.00E-06       Minor print level......         1
 Crash tolerance........     0.100       Pivot tolerance........  2.04E-11       Partial price..........         1
 Crash option...........         3       Elastic weight.........  1.00E+04       Prtl price section ( A)         4
                                         New superbasics........        99       Prtl price section (-I)         3
 
 The SQP Method
 --------------
 Minimize...............                 Cold start.............                 Proximal Point method..         1
 Nonlinear objectiv vars         4       Major optimality tol...  2.00E-06       Function precision.....  1.72E-13
 Unbounded step size....  1.00E+10       Superbasics limit......         4       Difference interval....  4.15E-07
 Unbounded objective....  1.00E+15       Reduced Hessian dim....         4       Central difference int.  5.57E-05
 Major step limit.......  2.00E+00       Derivative linesearch..                 Derivative level.......         3
 Major iterations limit.        50       Linesearch tolerance...   0.90000       Verify level...........         0
 Minor iterations limit.       500       Penalty parameter......  0.00E+00       Major Print Level......         1
 
 Hessian Approximation
 ---------------------
 Full-Memory Hessian....                 Hessian updates........  99999999       Hessian frequency......  99999999
                                                                                 Hessian flush..........  99999999
 
 Nonlinear constraints
 ---------------------
 Nonlinear constraints..         2       Major feasibility tol..  1.00E-06       Violation limit........  1.00E+06
 Nonlinear Jacobian vars         4
 
 Miscellaneous
 -------------
 LU factor tolerance....      1.10       LU singularity tol.....  2.04E-11       Timing level...........         0
 LU update tolerance....      1.10       LU swap tolerance......  1.03E-04       Debug level............         0
 LU partial  pivoting...                 eps (machine precision)  1.11E-16       System information.....        No
 
 
 
 
 Matrix statistics
 -----------------
               Total      Normal        Free       Fixed     Bounded
 Rows              3           3           0           0           0
 Columns           4           0           0           0           4
 
 No. of matrix elements                   12     Density     100.000
 Biggest                          1.0000E+00  (excluding fixed columns,
 Smallest                         0.0000E+00   free rows, and RHS)
 
 No. of objective coefficients             0
 
 Nonlinear constraints       2     Linear constraints       1
 Nonlinear variables         4     Linear variables         0
 Jacobian  variables         4     Objective variables      4
 Total constraints           3     Total variables          4
 
 
 
 The user has defined       8   out of       8   constraint gradients.
 The user has defined       4   out of       4   objective  gradients.
 
 Cheap test of user-supplied problem derivatives...
 
 The constraint gradients seem to be OK.
 
 -->  The largest discrepancy was    1.84E-07  in constraint     6
 
 
 The objective  gradients seem to be OK.
 
 Gradient projected in one direction   4.99993000077E+00
 Difference approximation              4.99993303560E+00
 
 
 
   Itns Major Minors    Step   nCon  Feasible   Optimal  MeritFunction     L+U BSwap     nS  condHz Penalty
      2     0      2              1   1.7E+00   2.8E+00  1.6000000E+01       7            2 1.0E+00         _  r
      4     1      2 1.0E+00      2   1.3E-01   3.2E-01  1.7726188E+01       8            1 6.2E+00 8.3E-02 _n r
      5     2      1 1.0E+00      3   3.7E-02   1.7E-01  1.7099571E+01       7            1 2.0E+00 8.3E-02 _s
      6     3      1 1.0E+00      4   2.2E-02   1.1E-02  1.7014005E+01       7            1 1.8E+00 8.3E-02 _
      7     4      1 1.0E+00      5   1.5E-04   6.0E-04  1.7014018E+01       7            1 1.8E+00 9.2E-02 _
      8     5      1 1.0E+00      6 ( 3.3E-07)  2.3E-05  1.7014017E+01       7            1 1.9E+00 3.6E-01 _
      9     6      1 1.0E+00      7 ( 4.2E-10)( 2.4E-08) 1.7014017E+01       7            1 1.9E+00 3.6E-01 _
 
 E04WDM EXIT   0 -- finished successfully
 E04WDM INFO   1 -- optimality conditions satisfied
 
 Problem name                      NLP
 No. of iterations                   9   Objective value      1.7014017287E+01
 No. of major iterations             6   Linear objective     0.0000000000E+00
 Penalty parameter           3.599E-01   Nonlinear objective  1.7014017287E+01
 No. of calls to funobj              8   No. of calls to funcon              8
 No. of superbasics                  1   No. of basic nonlinears             2
 No. of degenerate steps             0   Percentage                       0.00
 Max x                       2 4.7E+00   Max pi                      2 5.5E-01
 Max Primal infeas           0 0.0E+00   Max Dual infeas             3 4.8E-08
 Nonlinear constraint violn    2.7E-09
 
 
 Variable         State      Value       Lower bound     Upper bound   Lagr multiplier       Slack
 
 variable     1     LL    1.000000        1.000000        5.000000        1.087871            .
 variable     2     FR    4.743000        1.000000        5.000000            .             0.2570
 variable     3     FR    3.821150        1.000000        5.000000            .              1.179
 variable     4     FR    1.379408        1.000000        5.000000            .             0.3794
 
 
 Linear constrnt  State      Value       Lower bound     Upper bound   Lagr multiplier       Slack
 
 lincon       1     FR    10.94356          None          20.00000            .              9.056
 
 
 Nonlin constrnt  State      Value       Lower bound     Upper bound   Lagr multiplier       Slack
 
 nlncon       1     UL    40.00000          None          40.00000      -0.1614686         -0.2700E-08
 nlncon       2     LL    25.00000        25.00000          None         0.5522937         -0.2215E-08
 
 Final objective value =      17.014
 Optimal X =      1.00     4.74     3.82     1.38