A Non-Convex Analogue to Fenchel Duality

✍ Scribed by Mohammed Bachir

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 141 KB
• Volume: 181
• Category: Article
• ISSN: 0022-1236
• DOI: 10.1006/jfan.2000.3701

✦ Synopsis

We introduce and study a new notion of conjugacy, similar to Fenchel conjugacy, in a non-convex setting. Dual versions of S8 mulyan's classical result are established in the framework of this conjugacy, which reveal a relation between well-posed problems and the differentiability. As an application we deduce the generic Fre chet differentiability of the norm & }& in certain spaces of bounded continuous functions (i.e., Lip : (X ) for 0<:<1).