相关论文: Necessary conditions for linear convergence of ite…

We establish sufficient conditions for finite convergence of the alternating projections method for two non-intersecting and potentially nonconvex sets. Our results are based on a generalization of the concept of intrinsic transversality,…

In the setting of CAT(k) spaces, common fixed point iterations built from prox mappings (e.g. prox-prox, Krasnoselsky-Mann relaxations, nonlinear projected-gradients) converge locally linearly under the assumption of linear metric…

We consider the method of alternating projections for finding a point in the intersection of two closed sets, possibly nonconvex. Assuming only the standard transversality condition (or a weaker version thereof), we prove local linear…

Given two arbitrary closed sets in Euclidean space, a simple transversality condition guarantees that the method of alternating projections converges locally, at linear rate, to a point in the intersection. Exact projection onto nonconvex…

The article continues the study of the 'regular' arrangement of a collection of sets near a point in their intersection. Such regular intersection or, in other words, transversality properties are crucial for the validity of qualification…

The notion of Fej\'er monotonicity has proven to be a fruitful concept in fixed point theory and optimization. In this paper, we present new conditions sufficient for convergence of Fej\'er monotone sequences and we also provide…

While numerous extensions of Banach's fixed point theorem typically offer only sufficient conditions for the existence and uniqueness of a fixed point and the convergence of iterative sequences, this study introduces a generalization…

The idea of a finite collection of closed sets having "strongly regular intersection" at a given point is crucial in variational analysis. We show that this central theoretical tool also has striking algorithmic consequences. Specifically,…

We study the usage of regularity properties of collections of sets in convergence analysis of alternating projection methods for solving feasibility problems. Several equivalent characterizations of these properties are provided. Two…

We consider the popular and classical method of alternating projections for finding a point in the intersection of two closed sets. By situating the algorithm in a metric space, equipped only with well-behaved geodesics and angles (in the…

The numerical properties of algorithms for finding the intersection of sets depend to some extent on the regularity of the sets, but even more importantly on the regularity of the intersection. The alternating projection algorithm of von…

We derive conditions for the existence of fixed points of cone mappings without assuming scalability of functions. Monotonicity and scalability are often inseparable in the literature in the context of searching for fixed points of…

We consider the convergence rate of the alternating projection method for the nontransversal intersection of a semialgebraic set and a linear subspace. For such an intersection, the convergence rate is known as sublinear in the worst case.…

We observe that the characteristic polynomial of a linearly perturbed semidefinite matrix can be used to give the convergence rate of alternating projections for the positive semidefinite cone and a line. As a consequence, we show that such…

In this paper, we introduce and study a new extragradient iterative process for finding a common element of the set of fixed points of an infinite family of nonexpansive mappings and the set of solutions of a variational inequality for an…

We study the convergence of stochastic fixed point iterations in the consistent case (in the sense of Butnariu and Fl{\aa}m (1995)) in several different settings, under decreasingly restrictive regularity assumptions of the fixed point…

There are two basic ways of weakening the definition of the well-known metric regularity property by fixing one of the points involved in the definition. The first resulting property is called metric subregularity and has attracted a lot of…

This paper concerns generalized differential characterizations of maximal monotone set-valued mappings. Using advanced tools of variational analysis, we establish coderivative criteria for maximal monotonicity of set-valued mappings, which…

Fixed point iterations are a fundamental tool in numerical analysis and scientific computing for the approximation of solutions to nonlinear problems. Their convergence is often established via the Banach fixed point theorem, provided that…

We develop a framework for quantitative convergence analysis of Picard iterations of expansive set-valued fixed point mappings. There are two key components of the analysis. The first is a natural generalization of single-valued averaged…