- Iteration-Complexity of First-Order Augmented Lagrangian Methods for Convex Conic Programming Zhaosong Lu (zhaosongsfu.ca) Zirui Zhou (zrzhou01gmail.com) Abstract: In this paper we consider a class of convex conic programming. In particular, we propose an inexact augmented Lagrangian (I-AL) method for solving this problem, in which the augmented Lagrangian subproblems are solved approximately by a variant of Nesterov's optimal first-order method. We show that the total number of first-order iterations of the proposed I-AL method for computing an $\epsilon$-KKT solution is at most $\mathcal{O}(\epsilon^{-7/4})$. We also propose a modified I-AL method and show that it has an improved iteration-complexity $\mathcal{O}(\epsilon^{-1}\log\epsilon^{-1})$, which is so far the lowest complexity bound among all first-order I-AL type of methods for computing an $\epsilon$-KKT solution. Our complexity analysis of the I-AL methods is mainly based on an analysis on inexact proximal point algorithm (PPA) and the link between the I-AL methods and inexact PPA. It is substantially different from the existing complexity analyses of the first-order I-AL methods in the literature, which typically regard the I-AL methods as an inexact dual gradient method. Compared to the mostly related I-AL methods \cite{Lan16}, our modified I-AL method is more practically efficient and also applicable to a broader class of problems. Keywords: Convex conic programming, augmented Lagrangian method, first-order method, iteration complexity Category 1: Convex and Nonsmooth Optimization (Convex Optimization ) Citation: Zhaosong Lu and Zirui Zhou. Iteration-Complexity of First-Order Augmented Lagrangian Methods for Convex Conic Programming. arXiv:1803.09941, preprint, 2018. Download: [PDF]Entry Submitted: 03/28/2018Entry Accepted: 03/28/2018Entry Last Modified: 03/29/2018Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Optmization Society.