Ekeland's Variational Principle
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematical analysis, Ekeland''s variational principle 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.…mehr

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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematical analysis, Ekeland''s variational principle 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.