Modified Fejér sequences and applications

Junhong Lin, Lorenzo Rosasco, Silvia Villa () and Ding-Xuan Zhou
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Junhong Lin: Istituto Italiano di Tecnologia and Massachusetts Institute of Technology
Lorenzo Rosasco: Istituto Italiano di Tecnologia and Massachusetts Institute of Technology
Silvia Villa: Politecnico di Milano
Ding-Xuan Zhou: City University of Hong Kong

Computational Optimization and Applications, 2018, vol. 71, issue 1, No 5, 95-113

Abstract: Abstract In this note, we propose and study the notion of modified Fejér sequences. Within a Hilbert space setting, this property has been used to prove ergodic convergence of proximal incremental subgradient methods. Here we show that indeed it provides a unifying framework to prove convergence rates for objective function values of several optimization algorithms. In particular, our results apply to forward–backward splitting algorithm, incremental subgradient proximal algorithm, and the Douglas–Rachford splitting method including and generalizing known results.

Keywords: Convergence of first order methods; Proximal methods; Subgradient method; Fejér sequence (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10589-017-9962-1

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