Weak Sharp Minima: Characterizations and Sufficient Conditions

The problem of identifying weak sharp minima of order m, an important class of (possibly) nonisolated minima, is investigated in this paper. Some sufficient conditions for weak sharp minimality in nonsmooth mathematical programming are presented, and some characterizations of weak sharp minimality a...

Full description

Saved in:
Bibliographic Details
Published in:SIAM journal on control and optimization 1999, Vol.38 (1), p.219-236
Main Authors: Studniarski, Marcin, Ward, Doug E.
Format: Article
Language:English
Subjects:
Applied mathematics
Mathematical programming
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The problem of identifying weak sharp minima of order m, an important class of (possibly) nonisolated minima, is investigated in this paper. Some sufficient conditions for weak sharp minimality in nonsmooth mathematical programming are presented, and some characterizations of weak sharp minimality are obtained, with special attention given to orders one and two. It is also demonstrated that two of these sufficient conditions guarantee exactness of an l1 penalty function. A key role in this paper is played by two geometric concepts: the limiting proximal normal cone and a generalization of the contingent cone.
ISSN:0363-0129
1095-7138
DOI:10.1137/S0363012996301269