The Fenchel Duality Theorem in Fréchet Spaces

• 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
• Institution: Singapore Management University

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...