A Stochastic Successive Minimization Method for Nonsmooth Nonconvex Optimization with Applications to Transceiver Design in Wireless Communication Networks

• 成果类型: Article
• 署名作者: Razaviyayn, Meisam; Sanjabi, Maziar; Luo, Zhi-Quan
• 署名单位: Stanford University; University of Minnesota System; University of Minnesota Twin Cities
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-016-1021-7
• 发表日期: 2016
• 页码: 515-545
• 关键词: gradient methods; linear precoder; weighted mmse; CONVERGENCE; complexity; systems

摘要

Consider the problem of minimizing the expected value of a cost function parameterized by a random variable. The classical sample average approximation method for solving this problem requires minimization of an ensemble average of the objective at each step, which can be expensive. In this paper, we propose a stochastic successive upper-bound minimization method (SSUM) which minimizes an approximate ensemble average at each iteration. To ensure convergence and to facilitate computation, we require the approximate ensemble average to be a locally tight upper-bound of the expected cost function and be easily optimized. The main contributions of this work include the development and analysis of the SSUM method as well as its applications in linear transceiver design for wireless communication networks and online dictionary learning. Moreover, using the SSUM framework, we extend the classical stochastic (sub-)gradient method to the case of minimizing a nonsmooth nonconvex objective function and establish its convergence.