Primal-dual first-order methods with O (1/e) iteration-complexity for cone programming.

By Guanghui Lan, Zhaosong Lu, Renato D. C. Monteiro. 2011

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Citations in the corpus

Square-Root Lasso: Pivotal Recovery of Sparse Signals via Conic Programming (2010, methodology): “…us to implement the estimator using eﬃcient algorithmic methods, such as interior-point methods, which provide polynomial-time bounds on computational time [16, 17], and modern ﬁrst-order methods that have been recently extended to handle very large conic programming problems [14, 15, 11, 1].”
Templates for convex cone problems with applications to sparse signal recovery (2010, methodology): “– TS: Tseng’s single-projection simplification of N07 [63].”
Convex optimization under inexact first-order information (2009, methodology): “[32] proposed primal-dual convex (smooth and/or nonsmooth) minimization reformulations for general cone programming and compared three aforementioned first-order methods, namely, Nesterov’s optimal method [47, 50], Nesterov’s smooth approximation scheme [50], and Nemirovski’s prox-method [42], appli”
Adaptive Restart for Accelerated Gradient Schemes (2012, methodology): “In this paper we introduced a simple heuristic adaptive restart technique that can improve the convergence performance of accelerated gradient schemes for smooth convex optimization.”
A variational perspective on accelerated methods in optimization (2016, background): “[19] Guanghui Lan, Zhaosong Lu, and Renato Monteiro.”
Algorithms for stochastic optimization with expectation constraints (2016, methodology): “However these methods would require either the estimation of the optimal dual variables or iterations performed on the dual space (see [7], [23] and [20]).”
A Dual Approach for Optimal Algorithms in Distributed Optimization over Networks (2018, unknown): “Other variants of this method can be found in [47,48,49].”
Computational Optimal Transport: Complexity by Accelerated Gradient Descent Is Better Than by Sinkhorn's Algorithm (2018, background): “This algorithm can be considered as a primal-dual extension of accelerated mirror descent (Tseng, 2008; Lan et al., 2011).”
Randomized First-Order Methods for Saddle Point Optimization (2014, unknown): “, Lemma 6 of [25] and Lemma 2 of [16]) and the strong convexity of Jit(yit) (modulus 1) that for all y ∈ Y , 〈 −UitAx̄, yt+1 − y 〉 + Jit(y t+1 it )− Jit(yit) ≤ τt 2 ‖yit − y t it ‖(2)2 − τt 2 ‖y t it − y it ‖ 2 2 − 1+τt 2 ‖yit − y t+1 it ‖(2)2.”