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The Mehrotra-type predictor-corrector algorithm

The algorithmic framework of the Mehrotra-type predictor-corrector variant of the previous algorithm is as follows.



(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 tex2html_wrap_inline2393 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 tex2html_wrap_inline2119 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.