Open AccessConvergence rate of inertial Forward–Backward algorithm beyond Nesterov’s rule
Author(s) -
Vassilis Apidopoulos,
Jean–François Aujol,
Charles Dossal
Publication year - 2018
Publication title -
mathematical programming
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.358
H-Index - 131
eISSN - 1436-4646
pISSN - 0025-5610
DOI - 10.1007/s10107-018-1350-9
Subject(s) - mathematics , convergence (economics) , algorithm , rate of convergence , sequence (biology) , complement (music) , inertial frame of reference , function (biology) , relaxation (psychology) , operator (biology) , computer science , key (lock) , computer security , economic growth , chemistry , biology , genetics , psychology , social psychology , biochemistry , quantum mechanics , evolutionary biology , transcription factor , physics , complementation , economics , gene , phenotype , repressor
In this paper we study the convergence of an Inertial Forward–Backward algorithm, with a particular choice of an over-relaxation term. In particular we show that for a sequence of over-relaxation parameters, that do not satisfy Nesterov’s rule, one can still expect some relatively fast convergence properties for the objective function. In addition we complement this work by studying the convergence of the algorithm in the case where the proximal operator is inexactly computed with the presence of some errors and we give sufficient conditions over these errors in order to obtain some convergence properties for the objective function.
Accelerating Research
Robert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom
Address
John Eccles HouseRobert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom