Abstract
It is clear that Ekeland’s variational principle (Lemma 3.13) is an extremely useful form of the “maximality points lemma” (3.12); it was a key step in a sequence of fundamental results. As shown in Ekeland’s survey article [Ek], it has found application in such diverse areas as fixed-point theorems, nonlinear semigroups, optimization, mathematical programming, control theory and global analysis. Recall the statement: If ƒ is lower semicontinuous on E, ε τ 0 and x 0 is such that ƒ(x0) ≤ inf E ƒ + ε, then for any λ τ 0 there exists v ∈ E such that
Keywords
- Banach Space
- Maximal Monotone Operator
- Winning Strategy
- Nonempty Open Subset
- Bump Function
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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© 1993 Springer-Verlag Berlin Heidelberg
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(1993). Smooth variational principles, Asplund spaces, weak Asplund spaces. In: Convex Functions, Monotone Operators and Differentiability. Lecture Notes in Mathematics, vol 1364. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-46077-0_4
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DOI: https://doi.org/10.1007/978-3-540-46077-0_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-56715-8
Online ISBN: 978-3-540-46077-0
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