Thursday, 13:45 - 14:10 h, Room: H 2051

 

Sangho Kum
A geometric mean of parameterized arithmetic and harmonic means of convex functions

 

Abstract:
Recently Bauschke et al. (2008) introduced a new notion of proximal average, and studied this subject systemically from various viewpoints. The proximal average can be an attractive and powerful alternative to the classical arithmetic and
epigraphical averages in the context of convex analysis and optimization problems. The present work aims at providing a further development of the proximal average. For that purpose, exploiting the geometric mean of convex functions by Atteia and Rassouli (2001), we develop a new algorithmic self-dual operator for convex functions termed "the geometric mean of parameterized arithmetic and harmonic means of convex functions'', and investigate its essential properties.

 

Talk 2 of the invited session Thu.2.H 2051
"Variational analysis of optimal value functions and set-valued mappings with applications" [...]
Cluster 24
"Variational analysis" [...]

 

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