In this paper we study the effect of stochastic errors on two constrained
incremental sub-gradient algorithms. We view the incremental sub-gradient
algorithms as decentralized network optimization algorithms as applied to
minimize a sum of functions, when each component function is known only to a
particular agent of a distributed network. We first study the standard cyclic
incremental sub-gradient algorithm in which the agents form a ring structure
and pass the iterate in a cycle. We consider the method with stochastic errors
in the sub-gradient evaluations and provide sufficient conditions on the
moments of the stochastic errors that guarantee almost sure convergence when a
diminishing step-size is used. We also obtain almost sure bounds on the
algorithm's performance when a constant step-size is used. We then consider
\ram{the} Markov randomized incremental subgradient method, which is a
non-cyclic version of the incremental algorithm where the sequence of computing
agents is modeled as a time non-homogeneous Markov chain. Such a model is
appropriate for mobile networks, as the network topology changes across time in
these networks. We establish the convergence results and error bounds for the
Markov randomized method in the presence of stochastic errors for diminishing
and constant step-sizes, respectively.

研究随机误差对两个约束性增量次梯度算法的影响，并以分布式网络为基础，研究标准增量次梯度算法和随机误差下的方法。通过 Markov 随机增量次梯度方法，对移动网络拓扑变化的建模，研究其稳定性和误差上界。