On Quasi-Monotone Stochastic Variational Inequalities with Applications

This paper studies an efficient method for solving stochastic optimization problems formulated as stochastic variational inequalities with a quasi-monotone operator, where the cost function extends the classical monotone and pseudomonotone operators. Our proposed method iterates an adaptive stepsize that adjusts automatically without linesearch and includes a momentum term to accelerate the convergence. Each iteration requires only a single projection onto the feasible set, ensuring low computational complexity. Under standard assumptions, the algorithm achieves almost sure convergence and a proven convergence rate. Furthermore, numerical experiments demonstrate its superior performance, accuracy, stability, and efficiency compared with existing stochastic approximation schemes. We also apply the method to problems such as stochastic network bandwidth allocation, stochastic complementarity problems, and the networked stochastic Nash–Cournot game, showing its strength and practical usefulness. The obtained result is an extension of existing works in the literature.