arXiv subjects

Siqi Qu

Publications and source records attributed to Siqi Qu.

4 recordsLinked to original sources

arXiv2026

Inertial forward-backward algorithm with exterior penalization and Tikhonov regularization

In a real Hilbertian setting, we develop in this paper numerical splitting techniques guaranteeing strong convergence to the least norm solution of constrained variational inequalities. We develop a multiscale inertial forward-backward splitting algorithm for solving constrained monotone inclusion problems with multiscale penalization and vanishing Tikhonov regularization. The proposed framework accommodates smooth, nonsmooth, and mixed smooth--nonsmooth penalty operators, providing a unified treatment of a broad class of constrained monotone inclusion problems. In this general framework, we establish weak convergence of the generated iterates. By introducing a discrete Tikhonov central path, we further prove strong convergence to the minimum-norm solution of the problem under a mild constraint qualification condition on the problem data.

math.OC↗

arXiv2026

Asymptotic behaviour of coupled random dynamical systems with multiscale aspects

We examine a class of stochastic differential inclusions involving multiscale effects designed to solve a class of generalized variational inequalities. This class of problems contains constrained convex non-smooth optimization problems, constrained saddle-point problems and various equilibrium problems in economics and engineering. In order to respect constraints we adopt a penalty approach, introducing an explicit time-dependency into the evolution system. The resulting dynamics are described in terms of a non-autonomous stochastic evolution equation governed by maximally monotone operators in the drift and perturbed by a Brownian motion. We study the asymptotic behavior, as well as finite time convergence rates in terms of gap functions. The condition we use to prove convergence involves a Legendre transform of the function describing the set C, a condition first used by Attouch and Czarnecki (J. Differ. Equations, Vol. 248, Issue 6, 2010) in the context of deterministic evolution equations. We also establish a large deviations principle showing that individual trajectories exhibit exponential concentration around the solution set. Finally we show how our continuous-time approach relates to penalty-regulated algorithms of forward-backward type after performing a suitable Euler-Maruyama discretisation.

math.OC↗

arXiv2025

Asymptotic behavior of penalty dynamics for constrained variational inequalities

We propose a comprehensive framework for solving constrained variational inequalities via various classes of evolution equations displaying multi-scale aspects. In an infinite-dimensional Hilbertian framework, the class of dynamical systems we propose combine Tikhonov regularization and exterior penalization terms in order to induce strong convergence of trajectories to least norm solutions in the constrained domain. Our construction thus unifies the literature on regularization methods and penalty-based dynamical systems. An extension to a full splitting formulation of the constrained domain is also provided, with associated weak convergence results involving the Attouch-Czarnecki condition.

math.OC↗

arXiv2024

Tikhonov regularized exterior penalty dynamics for constrained variational inequalities

Solving equilibrium problems under constraints is an important problem in optimization and optimal control. In this context an important practical challenge is the efficient incorporation of constraints. We develop a continuous-time method for solving constrained variational inequalities based on a new penalty regulated dynamical system in a general potentially infinite-dimensional Hilbert space. In order to obtain strong convergence of the issued trajectory of our method, we incorporate an explicit Tikhonov regularization parameter in our method, leading to a class of time-varying monotone inclusion problems featuring multiscale aspects. Besides strong convergence, we illustrate the practical efficiency of our developed method in solving constrained min-max problems.

math.OC↗