Computer Science NASC Seminar

Analysis of Direct Searches for Non-Lipschitzian Functions

Luis Nunes Vicente, University of Coimbra

October 02, 2009 10:00AM
Warren Weaver Hall, Room 1302
251 Mercer Street
New York, NY, 10012-1110

Fall 2009 NASC Seminars Calendar


It is known that the Clarke generalized directional derivative is
nonnegative along the limit directions generated by directional
direct-search methods at a limit point of certain subsequences of
unsuccessful iterates, if the function being minimized is Lipschitz
continuous near the limit point.

In this talk we generalize this result for non-Lipschitzian functions
using Rockafellar generalized directional derivatives (upper subderivatives).
We show that Rockafellar derivatives are also nonnegative along the
limit directions of those subsequences of unsuccessful iterates when the
function values converge to the function value at the limit point.
This result is obtained assuming that the function is directionally
Lipschitzian with respect to the limit direction.

It is also possible under appropriate conditions to establish more
insightful results by showing that the sequence of points generated
by these methods eventually approaches the limit point along the
locally best branch or step function (when the number of steps is
equal to two).

The results are presented for constrained optimization and
illustrated numerically.

This is joint work with Ana Luisa Custodio (New Univ. Lisbon).

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