Title: Directionally Lipschitzian Mappings on Baire Spaces
Abstract: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 an...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.Read More
Title: $Directionally Lipschitzian Mappings on Baire Spaces
Abstract: 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.