caa a22 4500 605525668 CHVBK 20210128100759.0 cr unu---uuuuu 210128e20150801xx s 000 0 eng 10.1007/s10958-015-2482-6 doi (NATIONALLICENCE)springer-10.1007/s10958-015-2482-6 Balashov M. Department of Higher Mathematics, Moscow Institute of Physics and Technology, Institutskii per. 9, 141700, Dolgoprudny, Moscow region, Russia aut Maximization of a Function with Lipschitz Continuous Gradient [Elektronische Daten] [M. Balashov] In the present paper, we consider (nonconvex in the general case) functions that have Lipschitz continuous gradient. We prove that the level sets of such functions are proximally smooth and obtain an estimate for the constant of proximal smoothness. We prove that the problem of maximization of such function on a strongly convex set has a unique solution if the radius of strong convexity of the set is sufficiently small. The projection algorithm (similar to the gradient projection algorithm for minimization of a convex function on a convex set) for solving the problem of maximization of such a function is proposed. The algorithm converges with the rate of geometric progression. Springer Science+Business Media New York, 2015 Journal of Mathematical Sciences Springer US; http://www.springer-ny.com 209/1(2015-08-01), 12-18 1072-3374 209:1<12 2015 209 10958 https://doi.org/10.1007/s10958-015-2482-6 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/s10958-015-2482-6 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Balashov M. Department of Higher Mathematics, Moscow Institute of Physics and Technology, Institutskii per. 9, 141700, Dolgoprudny, Moscow region, Russia aut NATIONALLICENCE 773 0- Journal of Mathematical Sciences Springer US; http://www.springer-ny.com 209/1(2015-08-01), 12-18 1072-3374 209:1<12 2015 209 10958