This paper presents an investigation on the computational complexity of stochastic optimization problems. We discuss a scenariobased model which captures the important classes of two-stage stochastic combinatorial optimization, two-stage stochastic linear programming, and two-stage stochastic integer linear programming. This model can also be used to handle chance constraints, which are used in...

1. Introduction Many important real-world problems contain stochastic elements and require optimization. Stochastic programming and simulation-based optimization are two approaches used to address this issue. We do not explicitly discuss other related areas including stochastic control, stochas-tic dynamic programming, and Markov decision processes. We consider a stochastic optimization problem...

Abstract. In this paper, we present a new stochastic algorithm, namely the stochastic block mirror descent (SBMD) method for solving large-scale nonsmooth and stochastic optimization problems. The basic idea of this algorithm is to incorporate the block-coordinate decomposition and an incremental block averaging scheme into the classic (stochastic) mirror-descent method, in order to significant...