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• W2892301404 abstract "We develop novel non-ergodic alternating proximal augmented Lagrangian algorithms (NAPALA) to solve nonsmooth constrained convex optimization problems. Our approach relies on a novel combination of the augmented Lagrangian framework, partial alternating/linearization scheme, Nesterov's acceleration techniques, and homotopy strategies. Our algorithms have several new features compared to existing primal-dual methods. First, they have a Nesterov's acceleration step on the primal variables compared to the dual one in several existing methods. Second, they have an optimal O(1/k)-rate in non-ergodic sense without any smoothness or strong convexity-type assumption, where k is the iteration counter. Third, all the parameters are updated explicitly without heuristic tuning. Finally, they have O(1/k2)-ergodic or non-ergodic rate if one objective term is strongly convex while the problem remains nonstrongly convex. We verify our theoretical development via different numerical examples and compare our methods with some existing state-of-the-art algorithms." @default.
• W2892301404 created "2018-09-27" @default.
• W2892301404 creator A5003185205 @default.
• W2892301404 date "2018-12-03" @default.
• W2892301404 modified "2023-09-24" @default.
• W2892301404 title "Non-Ergodic Alternating Proximal Augmented Lagrangian Algorithms with Optimal Rates" @default.
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