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Directionally Lipschitzian Mappings on Baire Spaces

Published online by Cambridge University Press:  20 November 2018

J. M. Borwein  and
H. M. Stròjwas
J. M. Borwein
Affiliation:
Dalhousie University, Halifax, Nova Scotia
H. M. Stròjwas
Affiliation:
Carnegie-Mellon University, Pittsburgh, Pennsylvania
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Studies of optimization problems have led in recent years to definitions of several types of generalized directional derivatives. Those derivatives of primary interest in this paper were introduced and investigated by F. M. Clarke ([5], [6], [7], [8]), J. B. Hiriart-Urruty ([12]), Lebourg ([16], [17]), R. T. Rockafellar ([23], [24], [26], [27]), Penot ([21], [22]) among others.

In an attempt to explore in more detail relationships between various types of generalized directional derivatives we discovered some unexpected results which were not observed by the above mentioned authors. We are able to give simple conditions which characterize directionally Lipschitzian functions defined on a Baire metrizable locally convex topological vector space.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 36 , Issue 1 , 01 February 1984 , pp. 95 - 130
Copyright
Copyright © Canadian Mathematical Society 1984

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