nag_opt_sparse_nlp_jacobian (e04vjc) Example Program Results

NEA (the number of non-zero entries in A) =   4
  I     IAFUN(I)   JAVAR(I)          A(I)
----    --------   --------   -----------
  1         4         1       -1.0000e+00
  2         5         1        1.0000e+00
  3         4         2        1.0000e+00
  4         5         2       -1.0000e+00

NEG (the number of non-zero entries in G) =  10
  I     IGFUN(I)   JGVAR(I)
----    --------   --------
  1         1         1
  2         2         1
  3         3         1
  4         1         2
  5         2         2
  6         3         2
  7         6         3
  8         6         4
  9         1         3
 10         2         4
 
 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-06       Iteration limit........     10000
 Scale option...........         0       Minor optimality  tol..  1.00E-06       Minor print level......         1
 Crash tolerance........     0.100       Pivot tolerance........  2.05E-11       Partial price..........         1
 Crash option...........         3       Elastic weight.........  1.00E+04       Prtl price section ( A)         4
                                         New superbasics........        99       Prtl price section (-I)         5
 
 The SQP Method
 --------------
 Minimize...............                 Cold start.............                 Proximal Point method..         1
 Nonlinear objectiv vars         2       Objective Row..........         6       Function precision.....  1.72E-13
 Unbounded step size....  1.00E+20       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       Nonderiv.  linesearch..                 Derivative option......         0
 Major iterations limit.      1000       Linesearch tolerance...   0.90000       Verify level...........         0
 Minor iterations limit.       500       Penalty parameter......  0.00E+00       Major Print Level......         1
                                         Major optimality tol...  2.00E-06
 
 Hessian Approximation
 ---------------------
 Full-Memory Hessian....                 Hessian updates........  99999999       Hessian frequency......  99999999
                                                                                 Hessian flush..........  99999999
 
 Nonlinear constraints
 ---------------------
 Nonlinear constraints..         3       Major feasibility tol..  1.00E-06       Violation limit........  1.00E+06
 Nonlinear Jacobian vars         4
 
 Miscellaneous
 -------------
 LU factor tolerance....      3.99       LU singularity tol.....  2.05E-11       Timing level...........         0
 LU update tolerance....      3.99       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              5           2           0           3           0
 Columns           4           0           0           0           4
 
 No. of matrix elements                   12     Density      60.000
 Biggest                          1.0000E+00  (excluding fixed columns,
 Smallest                         0.0000E+00   free rows, and RHS)
 
 No. of objective coefficients             0
 
 Nonlinear constraints       3     Linear constraints       2
 Nonlinear variables         4     Linear variables         0
 Jacobian  variables         4     Objective variables      2
 Total constraints           5     Total variables          4
 
 
 
 The user has defined       0   out of      10   first  derivatives
 
 
 
   Itns Major Minors    Step   nCon  Feasible   Optimal  MeritFunction     L+U BSwap     nS  condHz Penalty
      3     0      3              1   8.0E+02   1.0E-00  0.0000000E+00      14            1 3.0E+07         _  r
      4     1      1 1.2E-03      2   4.0E+02   1.0E-00  1.7331708E+06      13            1 1.3E+07 5.1E+00 _n rl
      5     2      1 1.3E-03      3   2.7E+02   5.5E-01  1.7301151E+06      13                      5.1E+00 _s  l
      5     3      0 7.5E-03      4   8.8E+01   5.4E-01  8.8193381E+05      13                      2.8E+00 _   l
      5     4      0 2.3E-02      5   2.9E+01   5.3E-01  8.4262004E+05      13                      2.8E+00 _   l
      5     5      0 6.9E-02      6   8.9E+00   5.2E-01  7.3075567E+05      13                      2.8E+00 _   l
      6     6      1 2.2E-01      7   2.3E+00   8.0E+01  4.4817382E+05      13            1 1.2E+04 2.8E+00 _   l
      7     7      1 8.3E-01      8   1.7E-01   9.2E+00  2.4330986E+04      13            1 9.5E+03 2.8E+00 _   l
      8     8      1 1.0E+00      9   6.5E-03   4.0E+01  5.3126065E+03      13     1      1 1.3E+02 2.8E+00 _
      9     9      1 1.0E+00     10   4.6E-03   1.2E+01  5.1602362E+03      13            1 9.4E+01 2.8E+00 _
     10    10      1 1.0E+00     11   2.3E-04   6.1E-02  5.1265654E+03      13            1 9.6E+01 2.8E+00 _
     11    11      1 1.0E+00     12 ( 1.3E-08)  2.9E-04  5.1264981E+03      13            1 1.2E+02 2.8E+00 _      c
     12    11      2 1.0E+00     12 ( 1.3E-08)  2.7E-04  5.1264981E+03      13            1 1.2E+02 2.8E+00 _      c
     13    12      1 1.0E+00     13 ( 5.6E-13)  7.1E-05  5.1264981E+03      13            1 9.5E+01 2.8E+00 _      c
     14    13      1 1.0E+00     14 ( 1.8E-14)( 5.8E-11) 5.1264981E+03      13            1 9.5E+01 2.8E+00 _      c
 
 E04VHU EXIT   0 -- finished successfully
 E04VHU INFO   1 -- optimality conditions satisfied
 
 Problem name
 No. of iterations                  14   Objective value      5.1264981096E+03
 No. of major iterations            13   Linear objective     0.0000000000E+00
 Penalty parameter           2.780E+00   Nonlinear objective  5.1264981096E+03
 No. of calls to funobj            106   No. of calls to funcon            106
 Calls with modes 1,2 (known g)     14   Calls with modes 1,2 (known g)     14
 Calls for forward differencing     48   Calls for forward differencing     48
 Calls for central differencing     24   Calls for central differencing     24
 No. of superbasics                  1   No. of basic nonlinears             3
 No. of degenerate steps             0   Percentage                       0.00
 Max x                       2 1.0E+03   Max pi                      3 5.5E+00
 Max Primal infeas           0 0.0E+00   Max Dual infeas             1 5.6E-10
 Nonlinear constraint violn    1.5E-11
 
 Name                                    Objective Value      5.1264981096E+03
 
 Status         Optimal Soln             Iteration     14    Superbasics     1
 
 Objective               (Min)
 RHS
 Ranges
 Bounds
 
 Section 1 - Rows
 
  Number  ...Row.. State  ...Activity...  Slack Activity  ..Lower Limit.  ..Upper Limit.  .Dual Activity    ..i
 
       5  r      1    EQ      -894.80000         0.00000      -894.80000      -894.80000        -4.38698      1
       6  r      2    EQ      -894.80000         0.00000      -894.80000      -894.80000        -4.10563      2
       7  r      3    EQ     -1294.80000         0.00000     -1294.80000     -1294.80000        -5.46328      3
       8  r      4    BS        -0.51511         0.03489        -0.55000           None           .           4
       9  r      5    BS         0.51511         1.06511        -0.55000           None           .           5
 
 Section 2 - Columns
 
  Number  .Column. State  ...Activity...  .Obj Gradient.  ..Lower Limit.  ..Upper Limit.  Reduced Gradnt    m+j
 
       1  x      1    BS         0.11888          .             -0.55000         0.55000         0.00000      6
       2  x      2    BS        -0.39623          .             -0.55000         0.55000         0.00000      7
       3  x      3   SBS       679.94532         4.38698          .           1200.00000        -0.00000      8
       4  x      4    BS      1026.06713         4.10563          .           1200.00000         0.00000      9
Final objective value =      5126.5
Optimal X =      0.12     -0.40    679.95   1026.07