Iterative Splitting Methods for Stochastic Dynamic SVIs

TL;DR

This paper introduces new iterative splitting algorithms for stochastic dynamic variational inequalities in Banach spaces, effectively handling noise, time variation, and multi-agent coupling, with proven convergence and practical applications.

Contribution

It extends split variational inclusion methods to stochastic, dynamic, and multi-agent settings with convergence guarantees and adaptive techniques.

Findings

Algorithms demonstrate strong convergence in simulations.

Effective in resource allocation under uncertainty.

Numerical results validate theoretical claims.

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.