The strong Ekeland variational principle, the strong drop theorem and applications
type: Item
instance of: scholarly article
title: The strong Ekeland variational principle, the strong drop theorem and applications
zbMATH Open document ID: 0647.49009
DOI: 10.1016/0022-247X(88)90187-4
author: Pando G. Georgiev
published in: Journal of Mathematical Analysis and Applications
publication date: 1988-01-01T00:00:00Z
review text: Modified versions of Ekeland's variational principle [\textit{I. Ekeland}, ibid. 47, 324-353 (1974; Zbl 0286.49015)], of the drop theorem, of a lemma of \textit{R. R. Phelps} [Adv. Math. 13, 1-19 (1974; Zbl 0284.46015)] and of Penot's lower petal theorem [\textit{J.-P. Penot}, Nonlinear Anal., Theory Methods Appl. 10, 813-822 (1986; Zbl 0612.49011)] are proved, stating in addition, that every minimizing sequence is convergent. This is connected with the Tihonov and Hadamard well-posedness of minimization problems. All these versions are found to be equivalent to each other and to the corresponding original ones. As applications some generic results concerning well-posedness of minimization problems and single-valuedness and upper-semicontinuity of the metric projection are proved. As a corollary we have that almost all (in the Baire sense) sublinear and continuous functionals in a separable Banach space are Fréchet differentiable almost everywhere. Also the metric projection to a closed non-empty subset of a separable Bn of biped locomotion.
Mathematics Subject Classification ID: 49J45
Mathematics Subject Classification ID: 49J27
Mathematics Subject Classification ID: 49K40
zbMATH DE Number: 4056409
zbMATH Keywords: Ekeland's variational principle
zbMATH Keywords: drop theorem
zbMATH Keywords: Penot's lower petal theorem
zbMATH Keywords: well-posedness
zbMATH Keywords: minimization problems
zbMATH Keywords: metric projection
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4056409