Convex analysis | Variational principles | Theorems in functional analysis | Variational analysis

Ekeland's variational principle

In mathematical analysis, Ekeland's variational principle, discovered by Ivar Ekeland, is a theorem that asserts that there exist nearly optimal solutions to some optimization problems. Ekeland's principle can be used when the lower level set of a minimization problems is not compact, so that the Bolzano–Weierstrass theorem cannot be applied. The principle relies on the completeness of the metric space. The principle has been shown to be equivalent to completeness of metric spaces.In proof theory, it is equivalent to Π11CA0 over RCA0, i.e. relatively strong. It also leads to a quick proof of the Caristi fixed point theorem. (Wikipedia).

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Paul Shafer:Reverse mathematics of Caristi's fixed point theorem and Ekeland's variational principle

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Variation of parameters

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From playlist Differential equations

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Variational Principle Example

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From playlist Quantum Mechanics

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From playlist Differential Equations

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From playlist Differential equations

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Related pages

Effective domain | Metric space | Open set | Level set | Q.E.D. | Proper convex function | Bolzano–Weierstrass theorem | Optimization problem | Complete metric space | Mathematical analysis | Closed set | Proof theory | Reverse mathematics