Incremental constraint projection methods for variational inequalities

• 成果类型: Article
• 署名作者: Wang, Mengdi; Bertsekas, Dimitri P.
• 署名单位: Princeton University; Massachusetts Institute of Technology (MIT)
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-014-0769-x
• 发表日期: 2015
• 页码: 321-363
• 关键词: linear-programming approach; Approximation methods; common solutions; CONVERGENCE; algorithms

摘要

We consider the solution of strongly monotone variational inequalities of the form , for all . We focus on special structures that lend themselves to sampling, such as when is the intersection of a large number of sets, and/or is an expected value or is the sum of a large number of component functions. We propose new methods that combine elements of incremental constraint projection and stochastic gradient. These methods are suitable for problems involving large-scale data, as well as problems with certain online or distributed structures. We analyze the convergence and the rate of convergence of these methods with various types of sampling schemes, and we establish a substantial rate of convergence advantage for random sampling over cyclic sampling.