In mathematical analysis, Ekeland's variational principle, discovered by Ivar Ekeland, is a theorem that asserts that there exists nearly optimal solutions to some optimization problems.
Ekeland's variational principle can be used when the lower level set of a minimization problems is not compact, so that the Bolzano–Weierstrass theorem can not be applied. Ekeland's principle relies on the completeness of the metric space.
Ekeland's principle leads to a quick proof of the Caristi fixed point theorem.
Ekeland was associated with the Paris Dauphine University when he proposed this theorem.
Read more about Ekeland's Variational Principle: Statement of The Theorem
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