Zobrazeno 1 - 10
of 83
pro vyhledávání: '"Alexey A. Tret'yakov"'
Publikováno v:
Entropy, Vol 25, Iss 8, p 1112 (2023)
The paper describes an application of the p-regularity theory to Quadratic Programming (QP) and nonlinear equations with quadratic mappings. In the first part of the paper, a special structure of the nonlinear equation and a construction of the 2-fac
Externí odkaz:
https://doaj.org/article/8da2ee35a72d45c7a70fd5d01d4c0840
Autor:
Beata Medak, Alexey A Tret’yakov
Publikováno v:
Boundary Value Problems, Vol 2017, Iss 1, Pp 1-9 (2017)
Abstract The paper studies a solution existence problem of the nonlinear Duffing equation of the form F ( x , μ , β ) = x ″ + x + μ x 3 − β sin t = 0 , β > 0 , μ ≠ 0 , $$ F(x,\mu, \beta)=x''+x+\mu x^{3}-\beta\sin t = 0,\quad \beta > 0, \m
Externí odkaz:
https://doaj.org/article/a29d7606ded34d469abbed80aa6a24bd
Publikováno v:
Doklady Mathematics. 103:76-80
New properties of convex infinitely differentiable functions related to extremal problems are established. It is shown that, in a neighborhood of the solution, even if the Hessian matrix is singular at the solution point of the function to be minimiz
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::5b4ae065b27eb32dd43de280de623f3d
https://doi.org/10.1134/s1064562421020034
https://doi.org/10.1134/s1064562421020034
Publikováno v:
Computational Mathematics and Mathematical Physics. 60:1412-1421
Some fundamental optimization results are proved in new ways, which are not traditional and provide a new view of well-known results. Constructions of $$p$$ -regularity theory are used to justify the facts under consideration, and the 2-factor method
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::9bb4ee72a328bdc7eb869f63b66ef58f
https://doi.org/10.1134/s0965542520090080
https://doi.org/10.1134/s0965542520090080
Autor:
Beata Medak, Alexey A. Tret'yakov
Publikováno v:
Journal of Dynamics and Differential Equations. 33:1087-1107
This paper studies the problem of the continuous dependence of Van der Pol equation solutions with respect to the boundary conditions. We provide a new approach for the existence of such solutions via p-regularity theory. Several existence theorems a
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::6e42a3c121e44404c0b155a7af1bd51f
https://doi.org/10.1007/s10884-020-09849-0
https://doi.org/10.1007/s10884-020-09849-0
Publikováno v:
Optimization Methods and Software. 36:811-820
The paper illustrates connections between classical results of Analysis and Optimization. The focus is on new elementary proofs of Implicit Function Theorem, Lusternik's Theorem, and optimality con...
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::79a2baff98d2d94c90db56391557ebdb
https://doi.org/10.1080/10556788.2020.1731748
https://doi.org/10.1080/10556788.2020.1731748
Publikováno v:
Computational Mathematics and Mathematical Physics. 60:222-226
A numerical method combining a gradient technique with the projection onto a linear manifold is proposed for solving systems of linear inequalities. It is shown that the method converges in a finite number of iterations and its running time is estima
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::5d6d1f2e2716221234e8a8883d48365a
https://doi.org/10.1134/s0965542520020050
https://doi.org/10.1134/s0965542520020050
Autor:
Alexey A. Tret'yakov, B. Medak
Publikováno v:
Доклады Академии наук. 488:126-129
The problem of the existence of a continuous dependence of the solution of a boundary value problem on a parameter is considered. In this paper, it is proved that, in the presence of the p-regularity property, there exists a solution that continuousl
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::dccec2180d5f18c1903345c40eb35b3b
https://doi.org/10.31857/s0869-56524882126-129
https://doi.org/10.31857/s0869-56524882126-129
Publikováno v:
Russian Journal of Numerical Analysis and Mathematical Modelling. 34:163-174
In this paper we present a new solution method for underdetermined systems of nonlinear equations in a neighborhood of a certain point of the variety of solutions where the Jacoby matrix has incomplete rank. Such systems are usually called degenerate
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::0ee4bb65433b176b08e1f0e9ade738b9
https://doi.org/10.1515/rnam-2019-0014
https://doi.org/10.1515/rnam-2019-0014
Publikováno v:
Доклады Академии наук. 485:655-658
The classical Farkas theorem of the alternative is considered, which is widely used in various areas of mathematics and has numerous proofs and formulations. An entirely new elementary proof of this theorem is proposed. It is based on the considerati
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::58036e351eb92870fb63d1262a9fa395
https://doi.org/10.31857/s0869-56524856655-658
https://doi.org/10.31857/s0869-56524856655-658