On generalized Ekeland's variational principle and equivalent formulations for set-valued mappings

We propose a very weak type of generalized distance called weak τ-function and use it to weaken the assumptions about lower semicontinuity in existing formulations of Ekeland’s variational principle for a kind of minimizers of a set-valued mapping, which is different from the Pareto minimizer, and in recent results which are equivalent to Ekeland’s variational principle. Keywords Quasimetric spaces, locally convex spaces, weak τ-functions, Ekeland’s variational principle, K-lower semicontinity from above, lower closedness.

• Type: Journal
• Year: 2011
• Where: JGO
• Authors: Phan Quoc Khanh, D. N. Quy
• Keywords: JGO 2011, Locally Convex Spaces, Variational Principle, Weak τ-functions