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Linear semi-openness and the Lyusternik theorem

Authors
Journal
European Journal of Operational Research
0377-2217
Publisher
Elsevier
Publication Date
Volume
157
Issue
1
Identifiers
DOI: 10.1016/j.ejor.2003.08.011
Keywords
  • Set-Valued Mapping
  • Linear Semi-Openness
  • Linear Openness
  • Metric Regularity
  • Lyusternik Theorem
  • Contingent Cone
  • Piecewise Linear Function
  • Openness Bound
Disciplines
  • Mathematics

Abstract

Abstract A class of set-valued mappings called linearly semi-open mappings is introduced which properly contains the class of linearly open set-valued mappings. A stability result for linearly semi-open mappings is established. The main result is a Lyusternik type theorem. Sufficient conditions for linear semi-openness of processes are derived. To verify these conditions, the openness bounds of certain processes are computed. A representation of the openness bound of a locally Lipschitz function in a Clarke non-critical point is given. It is shown that continuous piecewise linear functions on R n are linearly semi-open under certain algebraic conditions.

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