Simultaneous almost minimization of convex functions and duals of results related to maximal monotonicity. (English) Zbl 1095.49503

Simons, S.

J. Convex Anal. 2, No. 1-2, 359-373 (1995).

It is known that on a nonreflexive Banach space \(E\) properties of convex functions defined on \(E\) and \(E^{*}\) are not completely symmetric. The aim of this interesting paper is to investigate several properties of proper convex and lower semi-continuous functions on \(E,\) involving their subdifferentials, which hold (with the same formulation) for the conjugates, their subdifferentials being considered as subsets of \(E\).

Reviewer: Constantin Zălinescu (MR 2000d:49021)

MSC:

49J45	Methods involving semicontinuity and convergence; relaxation
49N15	Duality theory (optimization)
90C46	Optimality conditions and duality in mathematical programming