The Fenchel Duality Theorem in Fréchet Spaces

The Fenchel Duality Theorem in Fréchet Spaces

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 res...

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Bibliographic Details
Main Author: RODRIGUES, Brian
Format: text
Language:English
Published: Institutional Knowledge at Singapore Management University 1990
Subjects:
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
Mathematics
Operations and Supply Chain Management
Online Access:https://ink.library.smu.edu.sg/lkcsb_research/2209
https://doi.org/10.1080/02331939008843516
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Institution: Singapore Management University
Language: English
Description
Summary: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.

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