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Journal of Convex Analysis 11 (2004), No. 2, 251--266
Copyright Heldermann Verlag 2004
Identifying Active Constraints via Partial Smoothness and Prox-Regularity
W. L. Hare
Dept. of Mathematics, Simon Fraser University, Burnaby, BC V5A 1S6, Canada,
whare@cecm.sfu.ca
A. S. Lewis
Dept. of Mathematics, Simon Fraser University, Burnaby, BC V5A 1S6, Canada,
aslewis@sfu.ca
Active set algorithms, such as the projected gradient method in
nonlinear optimization, are designed to "identify" the active
constraints of the problem in a finite number of iterations. Using
the notions of "partial smoothness" and "prox-regularity" we
extend work of Burke, More and Wright on identifiable surfaces
from the convex case to a general nonsmooth setting. We further
show how this setting can be used in the study of sufficient
conditions for local minimizers.
Keywords: nonlinear program, nonsmooth optimization, variational
analysis, partly smooth, prox-regular, identifiable surface, projected gradient.
MSC 2000: 91C30, 49K40, 65K10.
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