multifunction – Optimization Online

Slopes of multifunctions and extensions of metric regularity

Published: 2012/01/26, Updated: 2012/11/12

Nonsmooth Optimization error bound, metric regularity, multifunction, slope, variational analysis

This article aims to demonstrate how the definitions of slopes can be extended to multi-valued mappings between metric spaces and applied for characterizing metric regularity. Several kinds of local and nonlocal slopes are defined and several metric regularity properties for set-valued mappings between metric spaces are investigated. CitationPublished in Vietnam Journal of Mathematics 40:2&3(2012) 355-369. … Read more

About Stationarity and Regularity in Variational Analysis

Published: 2009/06/30, Updated: 2009/11/25

Alexander Y. Kruger

Convex and Nonsmooth Optimization asplund space, extremality, multifunction, normal cone, optimality, regularity, slope, stationarity, subdifferential

Stationarity and regularity concepts for the three typical for variational analysis classes of objects — real-valued functions, collections of sets, and multifunctions — are investigated. An attempt is maid to present a classification scheme for such concepts and to show that properties introduced for objects from different classes can be treated in a similar way. … Read more