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We provide a rule to calculate the subdifferential of the pointwise supremum of an arbitrary family of convex functions defined on a real locally convex topological vector space. Our formula is given exclusively in terms of the data functions, and does not require any assumption either on the index set on which the supremum is taken or on the involved… (More)

In this paper we study and compare the notions of uniform convexity of functions at a point and on bounded sets with the notions of total convexity at a point and sequential consistency of functions, respectively. We establish connections between these concepts of strict convexity in infinite dimensional settings and use the connections in order to obtain… (More)

In their paper " Duality of linear conic problems " A. Shapiro and A. Nemirovski considered two possible properties (A) and (B) for dual linear conic problems (P) and (D). The property (A) is " If either (P) or (D) is feasible, then there is no duality gap between (P) and (D) " , while property (B) is " If both (P) and (D) are feasible, then there is no… (More)

In this paper we introduce a convergence concept for closed convex subsets of a finite dimensional normed vector space. This convergence is called C-convergence. It is defined by appropriate notions of upper and lower limits. We compare this convergence with the well-known Painlevé–Kuratowski convergence and with scalar convergence. In fact, we show that a… (More)

Recently S.A. Clark published an interesting duality result in linear conic programming dealing with a convex cone that is not closed in which the usual (algebraic) dual problem is replaced by a topological dual with the aim to have zero duality gap under certain usual hypotheses met in mathematical finance. We present some examples to show that an extra… (More)