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

Meisam Razaviyayn, Maziar Sanjabi, Zhi Quan Luo

Research output: Contribution to journalArticlepeer-review

39 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)515-545
Number of pages31
JournalMathematical Programming
Volume157
Issue number2
DOIs
StatePublished - Jun 1 2016

Bibliographical note

Publisher Copyright:
© 2016, Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society.

Keywords

  • Sample average approximation
  • Stochastic beamformer design
  • Stochastic successive inner approximation
  • Stochastic successive upper-bound minimization

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