Monday, 15:45 - 16:10 h, Room: H 2038

 

Bin Wu
The Moreau-Yosida regularization of the Ky Fan k-norm related functions

Coauthors: Chao Ding, Defeng Sun, Kim-Chuan Toh

 

Abstract:
Matrix optimization problems (MOPs) involving the Ky Fan k-norm arise frequently in diverse fields such as matrix norm approximation, graph theory, and so on. In order to apply the proximal point algorithms to solve large scale MOPs involving the Ky Fan k-norm, we need to understand the first and second order properties of the Moreau-Yosida regularization of the Ky Fan k-norm function and the indicator function of its epigraph. As an initial step, we first study the counterparts of the vector k-norm related functions, including the metric projectors over the dual vector k-norm ball and the vector k-norm epigraph, and their directional derivatives and Fr├ęchet differentiability. We then use these results to study the corresponding properties for the Moreau-Yosida regularization of the Ky Fan k-norm epigraph indicator function.

 

Talk 2 of the invited session Mon.3.H 2038
"Matrix optimization" [...]
Cluster 4
"Conic programming" [...]

 

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