相关论文: Uniform Regularity of Set-Valued Mappings and Stab…

Metric regularity has emerged during last 2-3 decades as one of the central concepts of variational analysis. The roots of this concept go back to a circle of fundamental regularity ideas of classical analysis embodied in such results as…

We propose a unifying general framework of quantitative primal and dual sufficient and necessary error bound conditions covering linear and nonlinear, local and global settings. The function is not assumed to possess any particular…

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…

We investigate regularity properties of generalized conjugate functions induced by a general coupling function and the associated generalized proximal mapping. Our main results provide verifiable conditions ensuring local single-valuedness,…

We further investigate the uniform regularity property of collections of sets via primal and dual characterizing constants. These constants play an important role in determining convergence rates of projection algorithms for solving…

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…

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…

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…

We study the expanding properties of random perturbations of regular interval maps satisfying the summability condition of exponent one. Under very general conditions on the interval maps and perturbation types, we prove strong stochastic…

Several primal and dual characterizations of regularity properties of collections of sets in normed linear spaces are discussed. Relationships between regularity properties of collections of sets and those of set-valued mappings are…

For the existence of strong duality in convex optimization regularity conditions play an indisputable role. We mainly deal in this paper with regularity conditions formulated by means of different generalizations of the notion of interior…

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…

The main objective of this article is to provide an alternative approach to the central result of [Eldred, A. Anthony, Kirk, W. A., Veeramani, P., Proximal normal structure and relatively nonexpansive mappings, Studia Math., vol 171(3),…

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…

We find many conditions equivalent to the model-theoretical property $\lambda \stackrel{\kappa}{\Rightarrow} \mu$ introduced in [L1]. Our conditions involve uniformity of ultrafilters, compactness properties of products of topological…

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…

Bauschke and Moursi have recently obtained results that implicitly contain the fact that the composition of finitely many averaged mappings on a Hilbert space that have approximate fixed points also has approximate fixed points and thus is…

The present paper contains some investigations about a uniform variant of the notion of metric hemiregularity, the latter being a less explored property obtained by weakening metric regularity. The introduction of such a quantitative…

The subject of the present paper are stability properties of the solution set to set-valued inclusions. The latter are problems emerging in robust optimization and mathematical economics, which can not be cast in traditional generalized…

In these notes, we present a general result concerning the Lipschitz regularity of a certain type of set-valued maps often found in constrained optimization and control problems. The class of multifunctions examined in this paper is…