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Penalty Methods with Stochastic Approximation for Stochastic Nonlinear Programming

Xiao Wang (wangxiao***at***ucas.ac.cn)
Shiqian Ma (sqma***at***se.cuhk.edu.hk)
Ya-xiang Yuan (yyx***at***lsec.cc.ac.cn)

Abstract: In this paper, we propose a class of penalty methods with stochastic approximation for solving stochastic nonlinear programming problems. We assume that only noisy gradients or function values of the objective function are available via calls to a stochastic first-order or zeroth-order oracle. In each iteration of the proposed methods, we minimize an exact penalty function which is nonsmooth and nonconvex with only stochastic first-order or zeroth-order information available. Stochastic approximation algorithms are presented for solving this particular subproblem. The worst-case complexity of calls to the stochastic first-order (or zeroth-order) oracle for the proposed penalty methods for obtaining an $\epsilon$-stochastic critical point is analyzed.

Keywords: Stochastic Programming; Nonlinear Programming; Stochastic Approximation; Penalty Method; Global Complexity Bound

Category 1: Nonlinear Optimization

Category 2: Stochastic Programming


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Entry Submitted: 12/10/2013
Entry Accepted: 12/10/2013
Entry Last Modified: 05/18/2016

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