上海科技大学知识管理系统

Adaptive parameter strategies are crucial to enhancing robustness and ensuring practical applicability of penalty methods in  constrained optimization. However, in the context of  general  constrained stochastic optimization,  additional challenges  arise due to the randomness introduced by adaptive parameters. In this paper, we propose an Adaptive Stochastic Linearized augmented Lagrangian method (AdaStoL)  for solving nonconvex constrained stochastic optimization problem. AdaStoL employs a single-loop algorithmic  framework with dynamically updated penalty parameters based on the behavior of iterates. It combines  a recursive  momentum technique  along with clipped stochastic gradient computations to potentially reduce the random variance caused by stochasticity. We present a high-probability  oracle complexity analysis for the proposed algorithm to reach an $\epsilon$-KKT point.  Under certain constraint qualification conditions, we also investigate the global convergence properties  of AdaStoL regarding the stationarity residual and constraint violation at iterates when the penalty parameter sequence is unbounded and bounded, respectively. Preliminary numerical experiments results are also reported.