caa a22 4500 605525714 CHVBK 20210128100800.0 cr unu---uuuuu 210128e20150801xx s 000 0 eng 10.1007/s10958-015-2485-3 doi (NATIONALLICENCE)springer-10.1007/s10958-015-2485-3 Well-Posedness of Approximation and Optimization Problems for Weakly Convex Sets and Functions [Elektronische Daten] [G. Ivanov, M. Lopushanski] We consider the class of weakly convex sets with respect to a quasiball in a Banach space. This class generalizes the classes of sets with positive reach, proximal smooth sets and prox-regular sets. We prove the well-posedness of the closest points problem of two sets, one of which is weakly convex with respect to a quasiball M, and the other one is a summand of the quasiball −rM, where r ∈ (0, 1). We show that if a quasiball B is a summand of a quasiball M, then a set that is weakly convex with respect to the quasiball M is also weakly convex with respect to the quasiball B. We consider the class of weakly convex functions with respect to a given convex continuous function γ that consists of functions whose epigraphs are weakly convex sets with respect to the epigraph of γ. We obtain a sufficient condition for the well-posedness of the infimal convolution problem, and also a sufficient condition for the existence, uniqueness, and continuous dependence on parameters of the minimizer. Springer Science+Business Media New York, 2015 Ivanov G. Moscow Institute of Physics and Technology (State University), Moscow, Russia aut Lopushanski M. Moscow Institute of Physics and Technology (State University), Moscow, Russia aut Journal of Mathematical Sciences Springer US; http://www.springer-ny.com 209/1(2015-08-01), 66-87 1072-3374 209:1<66 2015 209 10958 https://doi.org/10.1007/s10958-015-2485-3 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10958-015-2485-3 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Ivanov G. Moscow Institute of Physics and Technology (State University), Moscow, Russia aut NATIONALLICENCE 700 1- Lopushanski M. Moscow Institute of Physics and Technology (State University), Moscow, Russia aut NATIONALLICENCE 773 0- Journal of Mathematical Sciences Springer US; http://www.springer-ny.com 209/1(2015-08-01), 66-87 1072-3374 209:1<66 2015 209 10958