nleqslv-iterationreport {nleqslv}R Documentation

Detailed iteration report of nleqslv

Description

The format of the iteration report provided by nleqslv when the trace component of the control parameter has been set to 1.

Details

All iteration reports consist of a series of columns with a header summarising the contents. Common column headers are

Iter
Iteration counter
Jac
Jacobian type. The jacobian type is indicated by N for a Newton jacobian or B for a Broyden updated matrix; optionally followed by the letter s indicating a totally singular matrix or the letter i indicating an ill-conditioned matrix. This is followed by a number in parentheses, indicating the inverse condition number of the matrix or the correction factor mu applied to make J'J+mu S'S not singular, where S is the diagonal scaling matrix consisting of the scaling factor for the x-values. This column will be blank when backtracking is active.
Fnorm
euclidean norm of function values / 2
Largest |f|
infinity norm of f(x) at the current point

A sample iteration report for qline is (some intercolumn space has been removed to make the table fit)

Iter         Jac Lambda        Ftarg         Fnorm   Largest |f|
   0                                  2.886812e+00  2.250000e+00
   1  N(9.6e-03) 1.0000 2.886235e+00  5.787362e+05  1.070841e+03
   1             0.1000 2.886754e+00  9.857947e+00  3.214799e+00
   1             0.0100 2.886806e+00  2.866321e+00  2.237878e+00
   2  B(2.2e-02) 1.0000 2.865748e+00  4.541965e+03  9.341610e+01
The column headed by Lambda shows the value of the linesearch parameter. The column headed by Ftarg follows from a sufficient decrease requirement and is the value below which Fnorm must drop if the current step is to be accepted.

A sample iteration report for dbldog is (some intercolumn space and the final column with header Largest |f| have been removed to make the table fit)

Iter         Jac   Lambda  Gamma    Eta   Dlt0   Dltn        Fnorm
   0                                                  2.886812e+00
   1  N(9.6e-03) C        0.9430 0.9544 0.4671 0.9343 1.699715e-01
   1             W 0.0833 0.9430 0.9544 0.9343 0.4671 1.699715e-01
   2  B(1.1e-02) W 0.1154 0.3564 0.4851 0.4671 0.4671 1.277667e-01
   3  B(7.3e-02) W 0.7879 0.6611 0.7289 0.4671 0.0759 5.067893e-01
   3             C        0.6611 0.7289 0.0759 0.1519 5.440250e-02
   4  B(8.3e-02) W 0.5307 0.1588 0.3271 0.1519 0.3037 3.576547e-02
   5  B(1.8e-01) N        0.5843 0.6674 0.2191 0.4383 6.566182e-03

After the column for the jacobian the letters indicate the following

C
a Cauchy or steepest descent is taken
W
a convex combination of the Cauchy and eta*Newton step is taken. The number in the column headed by Lambda is the weight of the partial Newton step.
P
a fraction of the full Newton step is taken. The number in the column headed by Eta is the fraction and is calculated as 0.8*gamma+0.2.
N
a normal full Newton step is taken

The number in the column headed by Gamma is an upper limit on the ratio of the length the steepest descent direction and the length of the Newton step. See Dennis and Schnabel (1996) pp.139ff for the details.

The column headed by Dlt0 gives the size of the trust region at the start of the current iteration. The column headed by Dltn gives the size of the trust region when the current step has been accepted by the dogleg algorithm. The size of the trust region is decreased when the actual reduction of the function value norm does not agree well with the predicted reduction from the linear approximation of the function. And increased when the actual and predicted reduction are sufficiently close.

Normally the initial trust region size is the same as the final trust region size of the previous iteration but the size of the trust region is restricted by the size of the current Newton step. So when full Newton steps are being taken, the trust region size at the start of an iteration may be less than the the final value of the previous iteration.

A sample iteration report for pwldog is (some intercolumn space has been removed to make the table fit)

Iter         Jac   Lambda   Dlt0   Dltn        Fnorm  Largest |f|
   0                                    2.886812e+00 2.250000e+00
   1  N(9.6e-03) C        0.4671 0.9343 1.699715e-01 5.421673e-01
   1             W 0.0794 0.9343 0.4671 1.699715e-01 5.421673e-01
   2  B(1.1e-02) W 0.0559 0.4671 0.4671 1.205661e-01 4.890487e-01
   3  B(7.3e-02) W 0.5662 0.4671 0.0960 4.119560e-01 7.254441e-01
   3             W 0.0237 0.0960 0.1921 4.426507e-02 2.139252e-01
   4  B(8.8e-02) W 0.2306 0.1921 0.3842 2.303135e-02 2.143943e-01
   4             W 0.4769 0.3842 0.1921 2.303135e-02 2.143943e-01
   5  B(1.9e-01) N        0.1375 0.2750 8.014508e-04 3.681498e-02
This is much simpler than the double dogleg report, since the (single) dogleg takes either a steepest descent step, a convex combination of the steepest descent and Newton directions or a full Newton step. The number in the column Lambda is the weight of the Newton step. It is a special case of the double dogleg method with eta equal to 1.

See Also

nleqslv


[Package nleqslv version 1.3 Index]