A generalization of Ekeland's \(\varepsilon\)-variational principle and its Borwein-Preiss smooth variant

DOI10.1006/jmaa.2000.6813zbMath0979.49014OpenAlexW2080484991MaRDI QIDQ1577987

Shuzhong Shi, Yongxin Li

Publication date: 5 February 2002

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jmaa.2000.6813

zbMATH Keywords

Ekeland's variational principleBorwein-Preiss smooth variational principle

Mathematics Subject Classification ID

Variational inequalities (49J40) Nonsmooth analysis (49J52) Fréchet and Gateaux differentiability in optimization (49J50) Differentiation theory (Gateaux, Fréchet, etc.) on manifolds (58C20)

Related Items (13)

Clarke-Ledyaev mean value inequalities in smooth Banach spaces ⋮ Borwein-Preiss vector variational principle ⋮ Equivalence of minimax and viscosity solutions of path-dependent Hamilton-Jacobi equations ⋮ Borwein-Preiss variational principle revisited ⋮ On generalized Ekeland's variational principle and equivalent formulations for set-valued mappings ⋮ Perturbed optimization on product spaces ⋮ Variational principles on topological spaces ⋮ Variational Principles in Analysis and Existence of Minimizers for Functions on Metric Spaces ⋮ Necessary conditions for constrained optimization problems with semicontinuous and continuous data ⋮ A linear perturbed Palais-Smale condition for lower semicontinuous functions on Banach spaces ⋮ Maximal and Variational Principles in Vector Spaces ⋮ Ekeland-type variational principle with applications to nonconvex minimization and equilibrium problems ⋮ On the equivalence of some basic principles in variational analysis

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• Generic Frechet-Differentiability and Perturbed Optimization Problems in Banach Spaces
• A Counterexample to Several Questions about Scattered Compact Spaces

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