13 citations · 26 across the 17 of their papers we have counts for
18 papers · 1 filter
Alternating Proximity Mapping Method for Strongly Convex-Strongly Concave Saddle-Point Problems
Hui Ouyang
This is a continuation of our previous work entitled \enquote{Alternating Proximity Mapping Method for Convex-Concave Saddle-Point Problems}, in which we proposed the alternating p…
A Note on the Convergence of the OGAProx
Hui Ouyang
In this note, we consider the Optimistic Gradient Ascent-Proximal Point Algorithm (OGAProx) proposed by Bo{ţ}, Csetnek, and Sedlmayer for solving a saddle-point problem associated…
Alternating Proximal Point Algorithm with Gradient Descent and Ascent Steps for Convex-Concave Saddle-Point Problems
Hui Ouyang
Inspired by the Optimistic Gradient Ascent-Proximal Point Algorithm (OGAProx) proposed by Bo{ţ}, Csetnek, and Sedlmayer for solving a saddle-point problem associated with a convex-…
Alternating Subgradient Methods for Convex-Concave Saddle-Point Problems
Hui Ouyang
We propose an alternating subgradient method with non-constant step sizes for solving convex-concave saddle-point problems associated with general convex-concave functions. We assu…
Alternating Proximity Mapping Method for Convex-Concave Saddle-Point Problems
Hui Ouyang
We proposed an iterate scheme for solving convex-concave saddle-point problems associated with general convex-concave functions. We demonstrated that when our iterate scheme is app…
Linear Convergence of Generalized Proximal Point Algorithms for Monotone Inclusion Problems
Hui Ouyang
We focus on the linear convergence of generalized proximal point algorithms for solving monotone inclusion problems. Under the assumption that the associated monotone operator is m…
On the Stability of Krasnosel'ski\vı-Mann Iterations
Hui Ouyang
Firstly, we invoke the weak convergence (resp. strong convergence) of translated basic methods involving nonexpansive operators to establish the weak convergence (resp. strong conv…
Weak and Strong Convergence of Generalized Proximal Point Algorithms with Relaxed Parameters
Hui Ouyang
In this work, we propose and study a framework of generalized proximal point algorithms associated with a maximally monotone operator. We indicate sufficient conditions on the regu…
Bregman Circumcenters: Monotonicity and Forward Weak Convergence
Hui Ouyang
Recently, we systematically studied the basic theory of Bregman circumcenters in another paper. In this work, we aim to apply Bregman circumcenters to optimization algorithms. Here…
Bregman circumcenters: basic theory
Hui Ouyang, Xianfu Wang
Circumcenters play an important role in the design and analysis of accelerating various iterative methods in optimization. In this work, we propose Bregman (pseudo-)circumcenters a…
Finite convergence of locally proper circumcentered methods
Hui Ouyang
In view of the great performance of circumcentered isometry methods for solving the best approximation problem, in this work we further investigate the locally proper circumcenter…
On angles between convex sets in Hilbert spaces
Heinz H. Bauschke, Hui Ouyang, Xianfu Wang
The notion of the angle between two subspaces has a long history, dating back to Friedrichs's work in 1937 and Dixmier's work on the minimal angle in 1949. In 2006, Deutsch and Hun…
Best approximation mappings in Hilbert spaces
Heinz H. Bauschke, Hui Ouyang, Xianfu Wang
The notion of best approximation mapping (BAM) with respect to a closed affine subspace in finite-dimensional space was introduced by Behling, Bello Cruz and Santos to show the lin…
Projecting onto intersections of halfspaces and hyperplanes
Hui Ouyang
It is well-known that the sequence of iterations of the composition of projections onto closed affine subspaces converges linearly to the projection onto the intersection of the af…
On the linear convergence of circumcentered isometry methods
Heinz H. Bauschke, Hui Ouyang, Xianfu Wang
The circumcentered Douglas--Rachford method (C--DRM), introduced by Behling, Bello Cruz and Santos, is an acceleration of the well-known Douglas-Rachford method (DRM) for finding t…
Circumcentered methods induced by isometries
Heinz H. Bauschke, Hui Ouyang, Xianfu Wang
Motivated by the circumcentered Douglas--Rachford method recently introduced by Behling, Bello Cruz and Santos to accelerate the Douglas--Rachford method, we study the properness o…
On circumcenter mappings induced by nonexpansive operators
Heinz H. Bauschke, Hui Ouyang, Xianfu Wang
We introduce the circumcenter mapping induced by a set of (usually nonexpansive) operators. One prominent example of a circumcenter mapping is the celebrated Douglas--Rachford spli…
On circumcenters of finite sets in Hilbert spaces
Heinz H. Bauschke, Hui Ouyang, Xianfu Wang
A well-known object in classical Euclidean geometry is the circumcenter of a triangle, i.e., the point that is equidistant from all vertices. The purpose of this paper is to provid…