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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 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)

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)

We use representations of maximal monotone operators for studying recession (or asymptotic) operators associated to maximal monotone operators. Such a concept is useful for dealing with un-boundedness. Dedicated to Alfred Auslender on the occasion of his sixty-fifth birthday