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Two results in convex analysis. (English) Zbl 0589.49007

Optimization and related fields, Proc. G. Stampacchia Int. Sch. Math., Erice/Italy 1984, Lect. Notes Math. 1190, 215-228 (1986).
[For the entire collection see Zbl 0581.00011.]
Two results in convex analysis are discussed. The first one is the theorem of Brønsted and Rockafellar on density of subdifferentiable points of l.s.c. convex functions and the second is the theorem of Toland on critical points of an l.s.c. convex functional and its conjugate. Both theorems are improved by using Ekeland’s variational principle.
Reviewer: S.Tersian

MSC:

49J45 Methods involving semicontinuity and convergence; relaxation
49N15 Duality theory (optimization)
90C25 Convex programming
46B99 Normed linear spaces and Banach spaces; Banach lattices

Citations:

Zbl 0581.00011