## Metric regularity and systems of generalized equations

The paper is devoted to a revision of the metric regularity property for mappings between metric or Banach spaces. Some new concepts are introduced: uniform metric regularity, metric regularity along a subspace, strong metric regularity for mappings into product spaces, when each component is perturbed independently. Regularity criteria are established based on a nonlocal version … Read more

## Stationarity and Regularity of Real-Valued Functions

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. Citation University of Ballarat, School of Information Technology and Mathematical … Read more

## About Regularity of Collections of Sets

The paper continues investigations of stationarity and regularity properties of set systems in normed spaces started in the previous paper of the author. It contains a summary of different characterizations (both primal and dual) of regularity and a list of sufficient conditions for a set system to be regular. Citation University of Ballarat, School of … Read more

## Stationarity and Regularity of Set Systems

Extremality, stationarity and regularity notions for a system of closed sets in a normed linear space are investigated. The equivalence of different abstract “extremal” settings in terms of set systems and multifunctions is proved. The dual necessary and sufficient conditions of weak stationarity (the Extended extremal principle) are presented for the case of an Asplund … Read more

## Weak Stationarity: Eliminating the Gap between Necessary and Sufficient Conditions

Starting from known necessary extremality conditions in terms of strict subdifferentials and normals the notion of weak stationarity is introduced. It is defined in terms of initial space elements. The necessary conditions become necessary and sufficient (for stationarity). Citation School of Information Technology and Mathematical Sciences, Centre of Information and Applied Optimization, University of Ballarat, … Read more