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

Modified Fejér sequences and applications

Lorenzo Rosasco;Silvia Villa;
2017

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
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11567/888673
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