Stochastic Penalty Function Methods for Nonsmooth Constrained Minimization

摘要

This paper presents a stochastic algorithm with proper stop-ping rules for nonsmooth inequality-constrained minimization prob-lems, The algorithm is based on an augmented Lagrangian dual problem transformed from a primal one, and it consists of two loops: an outer loop, which is the iteration for the approximate Lagrange multipliers, and an inner loop, which is a nonsmooth unconstrained minimization subroutine. Under mild assumptions, the algorithm is proved to be almost surely convergent.