Regularity on a Fixed Set
Александр Давидович Иоффе · SIAM Journal on Optimization · 2011
This paper is devoted to noninfinitesimal methods in nonlocal regularity theory for set-valued mappings between metric spaces and concentrates on studying two main interconnected topics: noninfinitesimal regularity criteria and fixed-points of set-valued mappings. A number of new results are proved, in particular those which cover and extend to a general metric setting some theorems viewed specifically as Banach-space results. In addition, a special technical interest in studying these two topics together is determined by the fact that each of them exploits a certain sequential iteration scheme (connected with Ekeland's principle in the first and Newton-type iterations in the second) and the extent to which each of the schemes can be effectively applied to the study of the other topic is at least unclear.