The Fenchel Duality Theorem in Fréchet Spaces

Alternative Title

The Fenchel duality theorem in Fréchet spaees

Publication Type

Journal Article

Publication Date

1990

Abstract

We generalize the Fenchel duality and inf-convolution theorems from convex optimization to Fréchet spaces. Our approach is simple and direct, and is to first prove a more general theorem in which we consider only one function and replace the product of spaces by an arbitrary Fréchet space. These results extend those obtained recently by Attouch and Brezis. Applications of our Generalizations are given.

Keywords

Locally convex space, Fréchet space, fully barreled, Legendbe-Fenchel transform, inf-convolution, effective domain, proper function, sublevel set, slater con-straint condition, subdifferential, normal cone, tangent cone, Kuhn-Tucker condition

Discipline

Mathematics | Operations and Supply Chain Management

Research Areas

Operations Management

Publication

Optimization

Volume

21

Issue

1

First Page

13

Last Page

22

ISSN

0233-1934

Identifier

10.1080/02331939008843516

Publisher

Taylor and Francis

Additional URL

https://doi.org/10.1080/02331939008843516

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