Maximization of a Function with Lipschitz Continuous Gradient
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| 024 | 7 | 0 | |a 10.1007/s10958-015-2482-6 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s10958-015-2482-6 | ||
| 100 | 1 | |a Balashov |D M. |u Department of Higher Mathematics, Moscow Institute of Physics and Technology, Institutskii per. 9, 141700, Dolgoprudny, Moscow region, Russia |4 aut | |
| 245 | 1 | 0 | |a Maximization of a Function with Lipschitz Continuous Gradient |h [Elektronische Daten] |c [M. Balashov] |
| 520 | 3 | |a 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. | |
| 540 | |a Springer Science+Business Media New York, 2015 | ||
| 773 | 0 | |t Journal of Mathematical Sciences |d Springer US; http://www.springer-ny.com |g 209/1(2015-08-01), 12-18 |x 1072-3374 |q 209:1<12 |1 2015 |2 209 |o 10958 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s10958-015-2482-6 |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/s10958-015-2482-6 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 100 |E 1- |a Balashov |D M. |u Department of Higher Mathematics, Moscow Institute of Physics and Technology, Institutskii per. 9, 141700, Dolgoprudny, Moscow region, 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), 12-18 |x 1072-3374 |q 209:1<12 |1 2015 |2 209 |o 10958 | ||