BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Local Convergence of the Heavy-ball Method and iPiano for Non-conv
 ex Optimization - Peter Ochs (Albert-Ludwigs-University Freiburg)
DTSTART:20170405T140000Z
DTEND:20170405T150000Z
UID:TALK71915@talks.cam.ac.uk
CONTACT:Carola-Bibiane Schoenlieb
DESCRIPTION:In this talk\, a local convergence result for abstract descent
  methods in\nnon-convex optimization is presented. In particular\, the ana
 lysis is\ntailored to inertial methods. The result can be summarized as fo
 llows:\nThe sequence of iterates is attracted by a local (or global) minim
 um\,\nstays in its neighborhood and converges within this neighborhood. Th
 is\nresult allows algorithms to exploit local properties of the objective\
 nfunction. Moreover\, it reveals an equivalence between iPiano (a\ngeneral
 ization of the Heavy-ball method) and inertial averaged/alternating proxim
 al\nminimization and projection methods. Key for this equivalence is the\n
 attraction to a local minimum within a common neighborhood and the fact th
 at\, for a prox-regular function\, the gradient of the Moreau envelope\nis
  locally Lipschitz continuous and expressible in terms of the proximal\nma
 pping. In a numerical feasibility problem\, the inertial alternating\nproj
 ection method significantly outperforms its non-inertial variants.
LOCATION:MR 14\, Centre for Mathematical Sciences
END:VEVENT
END:VCALENDAR