Asymptotic behaviour of stochastic inertial dynamics incorporating a Tikhonov regularization term

2025/12/17 by Schindler, Chiara
#34F05 #37N40 #60H10 #90C15 #90C25 #90C30 #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2512.15392

Abstract

In a separable Hilbert space, we study the minimization problem of a convex smooth function with Lipschitz continuous gradient whose evaluations are corrupted by random noise. To this end, we associate a stochastic inertial system that incorporates Tikhonov regularization with the optimization problem. We establish existence and uniqueness of a solution trajectory for this system. Then, we derive an upper bound on the expected value of an appropriate associated energy function given square-integrability of the diffusion σ_X before focusing on the particular case where the parameter function multiplied by the Tikhonov term is given by (1)/(t^r) for 0

Citations

• Long-Time Analysis of Stochastic Heavy Ball Dynamics for Convex Optimization and Monotone Equations
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• Mean Field Forward-Backward Stochastic Differential Equations

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• Long-Time Analysis of Stochastic Heavy Ball Dynamics for Convex Optimization and Monotone Equations
• Solving convex optimization problems via a second order dynamical system with implicit Hessian damping and Tikhonov regularization
• Inertial dynamics with vanishing Tikhonov regularization for multiobjective optimization