關於交替方向乘子法的近代研究

The Recent Study on ADMM

黃煥凱(Huan-Kai Huang)

指導教授 ： 李育杰 ； 王偉成

國立清華大學/理學院/數學系/碩士(2018年)

摘要

許多近幾年在機器學習中感興趣的問題，都可以被表示成凸最佳化問題。在大數據的時代，如何在分散式的網點中解決問題變得越來越重要。但藉由這個方法會產生隱私與安全議題。在本回顧，我們提供一個簡單但具有影響力的演算法：交替方向乘子法。交替方向乘子法可以在分散式的地點解決問題且保持隱私。 我們可以把交替方向乘子法當作是最新科技演算法的基準。

關鍵字

交替方向乘子法

並列摘要

Many problem of recent interest in machine learning can be represented to convex optimization problem. In big data era, its become more and more important to solve problem in distributed site. But by this way arise the privacy and security issue. In this review, we present a simple but powerful algorithm , the Alternating Direction Method of Multipliers (ADMM) which can solve the problem in distributed site and preserve privacy. ADMM can be viewed as the benchmark to the-state-of-the-art algorithm.

並列關鍵字

ADMM

參考文獻

[1] S. Boyd, N. Parikh, E. Chu, B. Peleato, J. Eckstein, et al., “Distributed optimiza- tion and statistical learning via the alternating direction method of multipliers,” Foundations and Trends® in Machine learning, vol. 3, no. 1, pp. 1–122, 2011.

[2] E.WeiandA.Ozdaglar,“Distributedalternatingdirectionmethodofmultipliers,” in Decision and Control (CDC), 2012 IEEE 51st Annual Conference on, pp. 5445– 5450, IEEE, 2012.

[3] T. Erseghe, “Distributed optimal power flow using admm,” IEEE transactions on power systems, vol. 29, no. 5, pp. 2370–2380, 2014.

[4] E. Ghadimi, A. Teixeira, I. Shames, and M. Johansson, “Optimal parameter selec- tion for the alternating direction method of multipliers (admm): quadratic prob- lems,” IEEE Transactions on Automatic Control, vol. 60, no. 3, pp. 644–658, 2015.

[5] S. Boyd and L. Vandenberghe, Convex optimization. Cambridge university press, 2004.