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The algorithmic framework of the Mehrotra-type predictor-corrector
variant of the previous algorithm is as follows.
Remarks.
- (a)
The default choices of expon for the AHO, HKM, NT, and GT
directions are expon = 3, 1, 1, 2, respectively.
We observed experimentally that
using expon = 2 for the HKM and NT directions seems
to be too aggressive, and usually results in slightly poorer numerical
stability when
is small compared to the choice expon = 1.
We should mention that the choice of the exponent e
in Algorithm IPC above is only a rough guide. The user might
want to explore other possibilities.
- (b) In our implementation, the user has the option to
switch from Algorithm IPF to Algorithm IPC
once the infeasibility measure
is
below a certain threshold specified by the
variable sw2PC_tol.
- (c) Once again, we also terminate if there is lack of progress
in either the predictor or corrector steps,
the primal or dual step-length is too small, or we get
an indication of primal or dual infeasibility.