arXiv subjects

Changchi Huang

Publications and source records attributed to Changchi Huang.

3 recordsLinked to original sources

arXiv2026

A primal-dual splitting algorithm for monotone inclusions with applications

In this paper, we study a broad class of structured monotone inclusion problems in real Hilbert spaces. We propose a novel primal-dual splitting algorithm for solving such inclusions, which accommodates multiple monotone operators and cocoercive terms, as well as a composite monotone operator involving the linear map. The algorithm combines forward evaluations for the cocoercive components with backward resolvent steps for the monotone operators and employs a dual update for the linear composition term. It generalizes and unifies several existing methods, while requiring only a single resolvent or operator evaluation per iteration. We prove weak convergence of the iterates under standard assumptions on monotonicity and cocoercivity. Furthermore, we establish strong convergence under a mild regularity condition, such as uniform monotonicity. Numerical experiments on image deblurring and denoising problems demonstrate the efficiency and flexibility of the proposed algorithm.

math.OC↗

arXiv2025

On $\alpha$-monotone operators and their resolvent in Banach spaces

This paper introduces a new definition of $\alpha$-monotone operators in real 2-uniformly convex and smooth Banach spaces. Based on this new definition, we establish several novel structural and analytical properties of such operators, which not only extend classical results from Hilbert spaces but also reveal new insights into the geometry of Banach spaces. In particular, we examine the resolvent of $\alpha$-maximal monotone operators and demonstrate how its behavior is consistent with, and generalizes, the well-known firmly nonexpansive property in the Hilbert space setting. Building upon this theoretical framework, we further investigate algorithmic applications. Specifically, we analyze the forward-reflected-backward splitting algorithm under the new $\alpha$-monotonicity assumption and prove its strong convergence as well as its $R$-linear convergence rate in real 2-uniformly convex and smooth Banach spaces.

math.FA↗

arXiv2025

H\"{o}lder property of the resolvent of a monotone operator in Banach spaces

Let $E$ be a Banach space, and let $J: E \to E^{*}$ denote the normalized duality mapping. In this paper, we establish an upper bound for $\|Jx - Jy\|$ in $q$-uniformly smooth Banach spaces, where the bound is expressed in terms of a relatively simple function of $\|x - y\|$. Subsequently, we derive the H\"{o}lder property of mappings of firmly nonexpansive type in 2-uniformly convex and $q$-uniformly smooth Banach spaces ($1<q\leq 2$). As an application, we apply this result to the resolvent of a monotone operator in Banach spaces.

math.FA↗