Well-Posedness of Approximation and Optimization Problems for Weakly Convex Sets and Functions
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| 024 | 7 | 0 | |a 10.1007/s10958-015-2485-3 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s10958-015-2485-3 | ||
| 245 | 0 | 0 | |a Well-Posedness of Approximation and Optimization Problems for Weakly Convex Sets and Functions |h [Elektronische Daten] |c [G. Ivanov, M. Lopushanski] |
| 520 | 3 | |a 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. | |
| 540 | |a Springer Science+Business Media New York, 2015 | ||
| 700 | 1 | |a Ivanov |D G. |u Moscow Institute of Physics and Technology (State University), Moscow, Russia |4 aut | |
| 700 | 1 | |a Lopushanski |D M. |u Moscow Institute of Physics and Technology (State University), Moscow, Russia |4 aut | |
| 773 | 0 | |t Journal of Mathematical Sciences |d Springer US; http://www.springer-ny.com |g 209/1(2015-08-01), 66-87 |x 1072-3374 |q 209:1<66 |1 2015 |2 209 |o 10958 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s10958-015-2485-3 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s10958-015-2485-3 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Ivanov |D G. |u Moscow Institute of Physics and Technology (State University), Moscow, Russia |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Lopushanski |D M. |u Moscow Institute of Physics and Technology (State University), Moscow, Russia |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Journal of Mathematical Sciences |d Springer US; http://www.springer-ny.com |g 209/1(2015-08-01), 66-87 |x 1072-3374 |q 209:1<66 |1 2015 |2 209 |o 10958 | ||