Random block-coordinate gradient projection algorithms

Chandramani Singh; Angelia Nedich; R. Srikant

doi:10.1109/CDC.2014.7039379

Random block-coordinate gradient projection algorithms

Chandramani Singh, Angelia Nedich, R. Srikant

Research output: Contribution to journal › Conference article › peer-review

Abstract

In this paper, we study gradient projection algorithms based on random partial updates of decision variables. These algorithms generalize random coordinate descent methods. We analyze these algorithms with and without assuming strong convexity of the objective functions. We also present an accelerated version of the algorithm based on Nesterov's two-step gradient method [1]. In each case, we prove convergence and provide a bound on the rate of convergence. We see that the randomized algorithms exhibit similar rates of convergence as their full gradient based deterministic counterparts.

Original language	English (US)
Article number	7039379
Pages (from-to)	185-190
Number of pages	6
Journal	Proceedings of the IEEE Conference on Decision and Control
Volume	2015-February
Issue number	February
DOIs	https://doi.org/10.1109/CDC.2014.7039379
State	Published - Jan 1 2014
Externally published	Yes
Event	2014 53rd IEEE Annual Conference on Decision and Control, CDC 2014 - Los Angeles, United States Duration: Dec 15 2014 → Dec 17 2014

ASJC Scopus subject areas

Control and Systems Engineering
Modeling and Simulation
Control and Optimization

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10.1109/CDC.2014.7039379

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title = "Random block-coordinate gradient projection algorithms",

abstract = "In this paper, we study gradient projection algorithms based on random partial updates of decision variables. These algorithms generalize random coordinate descent methods. We analyze these algorithms with and without assuming strong convexity of the objective functions. We also present an accelerated version of the algorithm based on Nesterov's two-step gradient method [1]. In each case, we prove convergence and provide a bound on the rate of convergence. We see that the randomized algorithms exhibit similar rates of convergence as their full gradient based deterministic counterparts.",

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AU - Nedich, Angelia

AU - Srikant, R.

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N2 - In this paper, we study gradient projection algorithms based on random partial updates of decision variables. These algorithms generalize random coordinate descent methods. We analyze these algorithms with and without assuming strong convexity of the objective functions. We also present an accelerated version of the algorithm based on Nesterov's two-step gradient method [1]. In each case, we prove convergence and provide a bound on the rate of convergence. We see that the randomized algorithms exhibit similar rates of convergence as their full gradient based deterministic counterparts.

AB - In this paper, we study gradient projection algorithms based on random partial updates of decision variables. These algorithms generalize random coordinate descent methods. We analyze these algorithms with and without assuming strong convexity of the objective functions. We also present an accelerated version of the algorithm based on Nesterov's two-step gradient method [1]. In each case, we prove convergence and provide a bound on the rate of convergence. We see that the randomized algorithms exhibit similar rates of convergence as their full gradient based deterministic counterparts.

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