Related papers: Metric Regularity. Theory and Applications - a sur…

Based on the idea of randomizing the traditional space theory of functional analysis, random functional analysis has been developed as functional analysis over random metric spaces, random normed modules and random locally convex modules.…

Metric regularity is among the central concepts of nonlinear and variational analysis, constrained optimization, and their numerous applications. However, metric regularity can be elusive for some important ill-posed classes of problems…

We propose a unifying general (i.e. not assuming the mapping to have any particular structure) view on the theory of regularity and clarify the relationships between the existing primal and dual quantitative sufficient and necessary…

Necessary and sufficient criteria for metric subregularity (or calmness) of set-valued mappings between general metric or Banach spaces are treated in the framework of the theory of error bounds for a special family of extended real-valued…

Since its introduction by J. Karamata, regular variation has evolved from a purely mathematical concept into a cornerstone of theoretical probability and data analysis. It is extensively studied and applied in different areas. Its…

The subject of this paper is regularity-preserving aggregation of regular norms on finite-dimensional linear spaces. Regular norms were introduced in [5] and are closely related to ``type 2'' spaces [9, Chapter 9] playing important role in…

In this work, we use the theory of error bounds to study metric regularity of the sum of two multifunctions, as well as some important properties of variational systems. We use an approach based on the metric regularity of epigraphical…

Although the property of strong metric subregularity of set-valued mappings has been present in the literature under various names and with various definitions for more than two decades, it has attracted much less attention than its older…

The regularity theory for variational inequalities over polyhedral sets developed in a series of papers by Robinson, Ralph and Dontchev-Rockafellar in the 90s has long become classics of variational analysis. But in the available proofs of…

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…

The paper is mainly devoted to systematic developments and applications of geometric aspects of second-order variational analysis that are revolved around the concept of parabolic regularity of sets. This concept has been known in…

Ioffe's criterion and various reformulations of it have become a~standard tool in proving theorems guaranteeing metric regularity of a (set-valued) mapping. First, we demonstrate that one should always use directly the so-called general…

This article delves into the study of the theory of regularized learning in Banach spaces for linear-functional data. It encompasses discussions on representer theorems, pseudo-approximation theorems, and convergence theorems. Regularized…

The aim of this article is to give a rather extensive, and yet nontechnical, account of the birth of the regularity theory for generalized minimal surfaces, of its various ramifications along the decades, of the most recent developments,…

A general nonlinear regularity model for a set-valued mapping $F:X\times R_+\rightrightarrows Y$, where $X$ and $Y$ are metric spaces, is considered using special iteration procedures, going back to Banach, Schauder, Lusternik and Graves.…

In this paper we aim to present two general results regarding, on one hand, the openness stability of set-valued maps and, on the other hand, the metric regularity behavior of the implicit multifunction related to a generalized variational…

In this article, we investigate nonlinear metric subregularity properties of set-valued mappings between general metric or Banach spaces. We demonstrate that these properties can be treated in the framework of the theory of (linear) error…

The paper concerns a new method to obtain a direct proof of the openness at linear rate/metric regularity of composite set-valued maps on metric spaces by the unification and refinement of several methods developed somehow separately in…

Regular sequences are natural generalisations of fixed points of constant-length substitutions on finite alphabets, that is, of automatic sequences. Using the harmonic analysis of measures associated with substitutions as motivation, we…

There is a basic paradigm, called here the radius of well-posedness, which quantifies the "distance" from a given well-posed problem to the set of ill-posed problems of the same kind. In variational analysis, well-posedness is often…