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Inexact proximal ϵ -subgradient methods for composite convex optimization problems
journal contributionposted on 2019-01-01, 00:00 authored by Reinier Diaz MillanReinier Diaz Millan, M P Machado
© 2019, Springer Science+Business Media, LLC, part of Springer Nature. We present two approximate versions of the proximal subgradient method for minimizing the sum of two convex functions (not necessarily differentiable). At each iteration, the algorithms require inexact evaluations of the proximal operator, as well as, approximate subgradients of the functions (namely: theϵ-subgradients). The methods use different error criteria for approximating the proximal operators. We provide an analysis of the convergence and rate of convergence properties of these methods, considering various stepsize rules, including both, diminishing and constant stepsizes. For the case where one of the functions is smooth, we propose an inexact accelerated version of the proximal gradient method, and prove that the optimal convergence rate for the function values can be achieved. Moreover, we provide some numerical experiments comparing our algorithm with similar recent ones.
JournalJournal of Global Optimization
Pagination1029 - 1060
Publication classificationC1.1 Refereed article in a scholarly journal
Splitting methodsOptimization problemE-SubdifferentialInexact methodsHilbert spaceAccelerated methodsScience & TechnologyTechnologyPhysical SciencesOperations Research & Management ScienceMathematics, AppliedMathematicsepsilon-SubdifferentialMONOTONE-OPERATORSGRADIENT METHODSALGORITHMCONVERGENCEEXTRAGRADIENTSUMComputation Theory and Mathematics