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

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 $$E$$.

### MSC:

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