slope – Page 2 – Optimization Online

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

Stationarity and Regularity of Real-Valued Functions

Published: 2005/11/30, Updated: 2006/10/08

Alexander Y. Kruger

Nonsmooth Optimization asplund space, nonsmooth analysis, normal cone, optimality, regularity, set-valued mapping, slope, stationarity, subdifferential

Different stationarity and regularity concepts for extended real-valued functions on metric spaces are considered in the paper. The properties are characterized in terms of certain local constants. A classification scheme for stationarity/regularity constants and corresponding concepts is proposed. The relations between different constants are established. CitationUniversity of Ballarat, School of Information Technology and Mathematical Sciences, … Read more