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pro vyhledávání: '"Balashov, Maxim"'
Autor:
Balashov, Maxim V.
Publikováno v:
Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика, Vol 23, Iss 1, Pp 4-10 (2023)
We consider the Lezanski – Polyak – Lojasiewicz inequality for a real-analytic function on a real-analytic compact manifold without boundary in finite-dimensional Euclidean space. This inequality emerged in 1963 independently in works of three au
Externí odkaz:
https://doaj.org/article/f5fb849b15fc46348fae3b9bcc5e44d7
Autor:
Balashov, Maxim, Tremba, Andrey
We analyse the convergence of the gradient projection algorithm, which is finalized with the Newton method, to a stationary point for the problem of nonconvex constrained optimization $\min_{x \in S} f(x)$ with a proximally smooth set $S = \{x \in R^
Externí odkaz:
http://arxiv.org/abs/1912.04660
Minimization of a smooth function on a sphere or, more generally, on a smooth manifold, is the simplest non-convex optimization problem. It has a lot of applications. Our goal is to propose a version of the gradient projection algorithm for its solut
Externí odkaz:
http://arxiv.org/abs/1906.11580
Autor:
Balashov, Maxim V., Repovš, Dušan
Publikováno v:
Journal of Convex Analysis 19:1 (2012), 171-183
We consider a certain metric on the space of all convex compacta in $\R^{n}$, introduced by A. Pli\'s. The set of strictly convex compacta is a complete metric subspace of the metric space of convex compacta with respect to this metric. We present so
Externí odkaz:
http://arxiv.org/abs/1112.4166
Autor:
Balashov, Maxim V., Repovš, Dušan
Publikováno v:
J. Math. Anal. Appl. 377:2 (2011), 754-761
We prove that in the Hilbert space every uniformly convex set with modulus of convexity of the second order at zero is an intersection of closed balls of fixed radius. We also obtain an estimate of this radius.
Externí odkaz:
http://arxiv.org/abs/1101.5685
Autor:
Balashov, Maxim V., Repovš, Dušan
Publikováno v:
J. Math. Anal. Appl. 374:2 (2011), 529-537
We consider polyhedral approximations of strictly convex compacta in finite dimensional Euclidean spaces (such compacta are also uniformly convex). We obtain the best possible estimates for errors of considered approximations in the Hausdorff metric.
Externí odkaz:
http://arxiv.org/abs/1010.2320
Autor:
Balashov, Maxim V., Repovš, Dušan
Publikováno v:
J. Math. Anal. Appl. 371:1 (2010), 113-127
We consider a definition of a weakly convex set which is a generalization of the notion of a weakly convex set in the sense of Vial and a proximally smooth set in the sense of Clarke, from the case of the Hilbert space to a class of Banach spaces wit
Externí odkaz:
http://arxiv.org/abs/1007.0162
Akademický článek
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Autor:
Balashov, Maxim V., Repovš, Dušan
Publikováno v:
J. Math. Anal. Appl. 360:1 (2009), 307-316
We continue to investigate cases when the Repov\v{s}-Semenov splitting problem for selections has an affirmative solution for continuous set-valued mappings. We consider the situation in infinite-dimensional uniformly convex Banach spaces. We use the
Externí odkaz:
http://arxiv.org/abs/0908.1216
Autor:
Balashov, Maxim V., Repovš, Dušan
Publikováno v:
J. Math. Anal. Appl. 355:1 (2009), 277-287.
We investigate when does the Repov\v{s}-Semenov Splitting problem for selections have an affirmative solution for continuous set-valued mappings in finite-dimensional Banach spaces. We prove that this happens when images of set-valued mappings or eve
Externí odkaz:
http://arxiv.org/abs/0807.3104