Directionally Lipschitzian Mappings on Baire Spaces

Borwein, J. M. ; Stròjwas, H. M.

Canadian journal of mathematics, Tome 36 (1984) no. 1, pp. 95-130

Résumé

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.

Détail

DOI : 10.4153/CJM-1984-008-7

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