Proceedings of the Steklov Institute of Mathematics最新文献_第2页

A Stable Solution of a Nonuniformly Perturbed Quadratic Minimization Problem by the Extragradient Method with Step Size Separated from Zero 用步长从零开始的外梯度法稳定求解非均匀扰动二次最小化问题

IF 0.5 4区数学

Proceedings of the Steklov Institute of Mathematics Pub Date : 2024-08-20 DOI: 10.1134/s0081543824030027

L. A. Artem’eva, A. A. Dryazhenkov, M. M. Potapov

{"title":"A Stable Solution of a Nonuniformly Perturbed Quadratic Minimization Problem by the Extragradient Method with Step Size Separated from Zero","authors":"L. A. Artem’eva, A. A. Dryazhenkov, M. M. Potapov","doi":"10.1134/s0081543824030027","DOIUrl":"https://doi.org/10.1134/s0081543824030027","url":null,"abstract":"A quadratic minimization problem is considered in Hilbert spaces under constraints given by a linear operator equation and a convex quadratic inequality. The main feature of the problem statement is that the practically available approximations to the exact linear operators specifying the criterion and the constraints converge to them only strongly pointwise rather than in the uniform operator norm, which makes it impossible to justify the use of the classical regularization methods. We propose a regularization method that is applicable in the presence of error estimates for approximate operators in pairs of other operator norms, which are weaker than the original ones. For each of the operators, the pair of corresponding weakened operator norms is obtained by strengthening the norm in the domain of the operator and weakening the norm in its range. The weakening of operator norms usually makes it possible to estimate errors in operators where this was fundamentally impossible in the original norms, for example, in the finite-dimensional approximation of a noncompact operator. From the original optimization formulation, a transition is made to the problem of finding a saddle point of the Lagrange function. The proposed numerical method for finding a saddle point is an iterative regularized extragradient two-stage procedure. At the first stage of each iteration, an approximation to the optimal value of the criterion is refined; at the second stage, the approximate solution with respect to the main variable is refined. Compared to the methods previously developed by the authors and working under similar information conditions, this method is preferable for practical implementation, since it does not require the gradient step size to converge to zero. The main result of the work is the proof of the strong convergence of the approximations generated by the method to one of the exact solutions to the original problem in the norm of the original space.\u0000","PeriodicalId":54557,"journal":{"name":"Proceedings of the Steklov Institute of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142190657","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Extensibility of Solutions of Nonautonomous Systems of Quadratic Differential Equations and Their Application in Optimal Control Problems 二次微分方程非自治系统解的可扩展性及其在优化控制问题中的应用

IF 0.5 4区数学

Proceedings of the Steklov Institute of Mathematics Pub Date : 2024-08-20 DOI: 10.1134/s008154382403009x

E. N. Khailov

{"title":"Extensibility of Solutions of Nonautonomous Systems of Quadratic Differential Equations and Their Application in Optimal Control Problems","authors":"E. N. Khailov","doi":"10.1134/s008154382403009x","DOIUrl":"https://doi.org/10.1134/s008154382403009x","url":null,"abstract":"The paper considers minimization problems with a free right endpoint on a given time interval for control affine systems of differential equations. For this class of problems, we study an estimate for the number of different zeros of switching functions that determine the form of the corresponding optimal controls. This study is based on analyzing nonautonomous linear systems of differential equations for switching functions and the corresponding auxiliary functions. Nonautonomous linear systems of third order are considered in detail. In these systems, the variables are changed so that the matrix of the system is transformed into a special upper triangular form. As a result, the number of zeros of the corresponding switching functions is estimated using the generalized Rolle’s theorem. In the case of a linear system of third order, this transformation is carried out using functions that satisfy a nonautonomous system of quadratic differential equations of the same order. The paper presents two approaches that ensure the extensibility of solutions of a nonautonomous system of quadratic differential equations to a given time interval. The first approach uses differential inequalities and Chaplygin’s comparison theorem. The second approach combines splitting a nonautonomous system of quadratic differential equations into subsystems of lower order and applying the quasi-positivity condition to these subsystems.\u0000","PeriodicalId":54557,"journal":{"name":"Proceedings of the Steklov Institute of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142190663","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Nonpronormal Subgroups of Odd Index in Finite Simple Linear and Unitary Groups 有限简单线性群和单元群中的奇数索引非正则子群

IF 0.5 4区数学

Proceedings of the Steklov Institute of Mathematics Pub Date : 2024-08-20 DOI: 10.1134/s0081543824030088

Wenbin Guo, N. V. Maslova, D. O. Revin

{"title":"Nonpronormal Subgroups of Odd Index in Finite Simple Linear and Unitary Groups","authors":"Wenbin Guo, N. V. Maslova, D. O. Revin","doi":"10.1134/s0081543824030088","DOIUrl":"https://doi.org/10.1134/s0081543824030088","url":null,"abstract":"A subgroup (H) of a group (G) is pronormal if, for each (gin G), the subgroups (H) and (H^{g}) are conjugate in (langle H,H^{g}rangle). Most of finite simple groups possess the following property ((ast)): each subgroup of odd index is pronormal in the group. The conjecture that all finite simple groups possess the property ((ast)) was established in 2012 in a paper by E.P. Vdovin and the third author based on the analysis of the proof that Hall subgroups are pronormal in finite simple groups. However, the conjecture was disproved in 2016 by A.S. Kondrat’ev together with the second and third authors. In a series of papers by Kondrat’ev and the authors published from 2015 to 2020, the finite simple groups with the property ((ast)) except finite simple linear and unitary groups with some constraints on natural arithmetic parameters were classified. In this paper, we construct series of examples of nonpronormal subgroups of odd index in finite simple linear and unitary groups over a field of odd characteristic, thereby making a step towards completing the classification of finite simple groups with the property ((ast)).\u0000","PeriodicalId":54557,"journal":{"name":"Proceedings of the Steklov Institute of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142190662","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

On the Continuity of the Optimal Time As a Function of the Initial State for Linear Controlled Objects with Integral Constraints on Controls 论带有控制积分约束的线性受控对象的最佳时间作为初始状态函数的连续性

IF 0.5 4区数学

Proceedings of the Steklov Institute of Mathematics Pub Date : 2024-08-20 DOI: 10.1134/s0081543824030118

M. S. Nikol’skii

{"title":"On the Continuity of the Optimal Time As a Function of the Initial State for Linear Controlled Objects with Integral Constraints on Controls","authors":"M. S. Nikol’skii","doi":"10.1134/s0081543824030118","DOIUrl":"https://doi.org/10.1134/s0081543824030118","url":null,"abstract":"A traditional object of study in the mathematical theory of optimal control is a controlled object with geometric constraints on the control vector (u). At the same time, it turns out that sometimes it is more convenient to impose integral constraints on the control vector (u). For example, in the theory of automatic design of optimal controllers, it is sometimes assumed that the control vector (u) is not subject to any geometric constraints, but there is a requirement that the control (u(t)) and its squared length (|u(t)|^{2}) are Lebesgue summable on the corresponding interval. This circumstance, as well as the fact that the performance index has the form of a quadratic functional, makes it possible to construct an optimal control under rather broad assumptions. Quadratic integral constraints on controls can be interpreted as some energy constraints. Controlled objects under integral constraints on the controls are given quite a lot of attention in the mathematical literature on control theory. We mention the works of N.N. Krasovskii, E.B. Lee, L. Markus, A.B. Kurzhanskii, M.I. Gusev, I.V. Zykov, and their students. The paper studies a linear time-optimal problem, in which the terminal set is the origin, under an integral constraint on the control. Sufficient conditions are obtained under which the optimal time as a function of the initial state (x_{0}) is continuous.\u0000","PeriodicalId":54557,"journal":{"name":"Proceedings of the Steklov Institute of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142190665","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Integro-Differential Equations of Gerasimov Type with Sectorial Operators 带扇形算子的格拉西莫夫式积分微分方程

IF 0.5 4区数学

Proceedings of the Steklov Institute of Mathematics Pub Date : 2024-08-20 DOI: 10.1134/s0081543824030076

V. E. Fedorov, A. D. Godova

引用次数: 0

On Some Complements to Liu’s Theory 论对刘氏理论的一些补充

IF 0.5 4区数学

Proceedings of the Steklov Institute of Mathematics Pub Date : 2024-08-20 DOI: 10.1134/s0081543824030015

B. I. Ananyev

引用次数: 0

Reidemeister Torsion for Vector Bundles on $$mathbb{P}^{1}_{mathbb{Z}}$$ $$mathbb{P}^{1}_{mathbb{Z}}$ 上向量束的雷德梅斯特扭转

IF 0.5 4区数学

Proceedings of the Steklov Institute of Mathematics Pub Date : 2024-08-20 DOI: 10.1134/s008154382403012x

V. M. Polyakov

引用次数: 0

On the Identification of Control Failures by the Dynamic Regularization Method 论用动态正则化方法识别控制故障

IF 0.5 4区数学

Proceedings of the Steklov Institute of Mathematics Pub Date : 2024-08-20 DOI: 10.1134/s0081543824030106

V. I. Maksimov, Yu. S. Osipov

引用次数: 0

Bell’s Inequality, Its Physical Origins, and Generalization 贝尔不等式、其物理起源和一般化

IF 0.5 4区数学

Proceedings of the Steklov Institute of Mathematics Pub Date : 2024-07-11 DOI: 10.1134/s0081543824010103

V. A. Zorich

引用次数: 0

On Local Continuity of Characteristics of Composite Quantum Systems 论复合量子系统特性的局部连续性

IF 0.5 4区数学

Proceedings of the Steklov Institute of Mathematics Pub Date : 2024-07-11 DOI: 10.1134/s0081543824010206

M. E. Shirokov

引用次数: 0