Iterative Splitting Methods for Stochastic Dynamic SVIs

Abstract

This paper extends split variational inclusion problems to dynamic, stochastic, and multi-agent systems in Banach spaces. We propose novel iterative algorithms to handle stochastic noise, time-varying operators, and coupled variational inclusions. Leveraging advanced splitting techniques and self-adaptive rules, we establish weak convergence under minimal assumptions on operator monotonicity. Numerical experiments demonstrate the efficacy of our algorithms, particularly in resource allocation and optimization under uncertainty.