Extremality, Stationarity and Generalized Separation of Collections of Sets

Abstract

The core arguments used in various proofs of the extremal principle and its extensions as well as in primal and dual characterizations of approximate stationarity and transversality of collections of sets are exposed, analyzed and refined, leading to a unifying theory, encompassing all existing approaches to obtaining 'extremal' statements. For that, we examine and clarify quantitative relationships between the parameters involved in the respective definitions and statements. Some new characterizations of extremality properties are obtained.

arXiv comment51 pages

References in corpus (6)

• Transversality and alternating projections for nonconvex sets
• Set Regularities and Feasibility Problems
• About subtransversality of collections of sets
• Quantitative Characterizations of Regularity Properties of Collections of Sets
• About uniform regularity of collections of sets
• About Extensions of the Extremal Principle

Cited by in corpus (6)

• Transversality Properties: Primal Sufficient Conditions
• Extremality of families of sets
• Sequential Extremal Principle and Necessary Conditions for Minimizing Sequences
• Necessary Conditions for Non-Intersection of Collections of Sets
• Generalized Separation of Collections of Sets
• Extremality of families of sets and set-valued optimization