Proceedings of the Steklov Institute of Mathematics最新文献

The Method of Comparison with a Model Equation in the Study of Inclusions in Vector Metric Spaces 矢量公设空间夹杂物研究中的模型方程比较法

IF 0.5 4区数学

Proceedings of the Steklov Institute of Mathematics Pub Date : 2024-08-20 DOI: 10.1134/s0081543824030180

E. S. Zhukovskiy, E. A. Panasenko

{"title":"The Method of Comparison with a Model Equation in the Study of Inclusions in Vector Metric Spaces","authors":"E. S. Zhukovskiy, E. A. Panasenko","doi":"10.1134/s0081543824030180","DOIUrl":"https://doi.org/10.1134/s0081543824030180","url":null,"abstract":"For a given multivalued mapping (F:Xrightrightarrows Y) and a given element (tilde{y}in Y), the existence of a solution (xin X) to the inclusion (F(x)nitilde{y}) and its estimates are studied. The sets (X) and (Y) are endowed with vector-valued metrics (mathcal{P}_{X}^{E_{+}}) and (mathcal{P}_{Y}^{M_{+}}), whose values belong to cones (E_{+}) and (M_{+}) of a Banach space (E) and a linear topological space (M), respectively. The inclusion is compared with a “model” equation (f(t)=0), where (f:E_{+}to M). It is assumed that (f) can be written as (f(t)equiv g(t,t)), where the mapping (g:{E}_{+}times{E}_{+}to M) orderly covers the set ({0}subset M) with respect to the first argument and is antitone with respect to the second argument and (-g(0,0)in M_{+}). It is shown that, in this case, the equation (f(t)=0) has a solution (t^{*}in E_{+}). Further, conditions on the connection between (f(0)) and (F(x_{0})) and between the increments of (f(t)) for (tin[0,t^{*}]) and the increments of (F(x)) for all (x) in the ball of radius (t^{*}) centered at (x_{0})\u0000for some (x_{0}) are formulated, and it is shown that the inclusion has a solution in the ball under these conditions. The results on the operator inclusion obtained in the paper are applied to studying an integral inclusion.\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":"142190672","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

The Perturbation Method and Regularization of the Lagrange Multiplier Rule in Convex Constrained Optimization Problems 凸约束优化问题中的扰动法和拉格朗日乘数规则的正规化

IF 0.5 4区数学

Proceedings of the Steklov Institute of Mathematics Pub Date : 2024-08-20 DOI: 10.1134/s0081543824030155

M. I. Sumin

{"title":"The Perturbation Method and Regularization of the Lagrange Multiplier Rule in Convex Constrained Optimization Problems","authors":"M. I. Sumin","doi":"10.1134/s0081543824030155","DOIUrl":"https://doi.org/10.1134/s0081543824030155","url":null,"abstract":"We consider a regularization of the Lagrange multiplier rule (LMR) in the nondifferential form in a convex constrained optimization problem with an operator equality constraint in a Hilbert space and a finite number of functional inequality constraints. The objective functional of the problem is assumed to be strongly convex, and the convex closed set of its admissible elements also belongs to a Hilbert space. The constraints of the problem contain additively included parameters, which enables using the so-called perturbation method to study it. The main purpose of the regularized LMR is the stable generation of generalized minimizing sequences (GMSs), which approximate the exact solution of the problem using extremals of the regular Lagrange functional. The regularized LMR itself can be interpreted as a GMS-generating (regularizing) operator, which assigns to each set of input data of the constrained optimization problem the extremal of its corresponding regular Lagrange functional, in which the dual variable is generated following one or another procedure for stabilizing the dual problem. The main attention is paid to (1) studying the connection between the dual regularization procedure and the subdifferential properties of the value function of the original problem; (2) proving the convergence of this procedure in the case of solvability of the dual problem; (3) an appropriate update of the regularized LMR; (4) obtaining the classical LMR as a limiting version of its regularized analog. ","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":"142190669","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

Sufficient Optimality Conditions for Hybrid Systems of Variable Dimension with Intermediate Constraints 具有中间约束条件的可变维度混合系统的充分最优条件

IF 0.5 4区数学

Proceedings of the Steklov Institute of Mathematics Pub Date : 2024-08-20 DOI: 10.1134/s0081543824030052

A. S. Bortakovskii

引用次数: 0

On a Control Reconstruction Problem with Nonconvex Constraints 关于具有非凸约束条件的控制重构问题

IF 0.5 4区数学

Proceedings of the Steklov Institute of Mathematics Pub Date : 2024-08-20 DOI: 10.1134/s0081543824030143

N. N. Subbotina, E. A. Krupennikov

引用次数: 0

Package Guidance Problem for a Fractional-Order System 分数阶系统的包引导问题

IF 0.5 4区数学

Proceedings of the Steklov Institute of Mathematics Pub Date : 2024-08-20 DOI: 10.1134/s0081543824030167

P. G. Surkov

{"title":"Package Guidance Problem for a Fractional-Order System","authors":"P. G. Surkov","doi":"10.1134/s0081543824030167","DOIUrl":"https://doi.org/10.1134/s0081543824030167","url":null,"abstract":"The problem of guaranteed closed-loop guidance to a given set at a given time is studied for a linear dynamic control system described by differential equations with a fractional derivative of the Caputo type. The initial state is a priori unknown, but belongs to a given finite set. The information on the position of the system is received online in the form of an observation signal. The solvability of the guidance problem for the control system is analyzed using the method of Osipov–Kryazhimskii program packages. The paper provides a brief overview of the results that develop the program package method and use it in guidance problems for various classes of systems. This method allows us to connect the solvability condition of the guaranteed closed-loop guidance problem for an original system with the solvability condition of the open-loop guidance problem for a special extended system. Following the technique of the program package method, a criterion for the solvability of the considered guidance problem is derived for a fractional-order system. In the case where the problem is solvable, a special procedure for constructing a guiding program package is given. The developed technique for analyzing the guaranteed closed-loop guidance problem and constructing a guiding control for an unknown initial state is illustrated by the example of a specific linear mechanical control system with a Caputo fractional derivative.\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":"142190670","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

Finite Groups with $$mathbb{P}$$ -Subnormal Schmidt Subgroups 具有 $$mathbb{P}$ -Subnormal Schmidt 子群的有限群

IF 0.5 4区数学

Proceedings of the Steklov Institute of Mathematics Pub Date : 2024-08-20 DOI: 10.1134/s0081543824030179

Xiaolan Yi, Zhuyan Xu, S. F. Kamornikov

引用次数: 0

On Modeling a Solution of Systems with Constant Delay Using Controlled Models 论利用受控模型为具有恒定延迟的系统解决方案建模

IF 0.5 4区数学

Proceedings of the Steklov Institute of Mathematics Pub Date : 2024-08-20 DOI: 10.1134/s0081543824030040

M. S. Blizorukova, V. I. Maksimov

引用次数: 0

Continuous Dependence of Sets in a Space of Measures and a Program Minimax Problem 度量空间中集合的连续依赖性和程序最小问题

IF 0.5 4区数学

Proceedings of the Steklov Institute of Mathematics Pub Date : 2024-08-20 DOI: 10.1134/s0081543824030064

A. G. Chentsov, D. A. Serkov

引用次数: 0

Control of Acceleration of a Dynamic Object by the Modified Linear Tangent Law in the Presence of a State Constraint 在状态约束条件下利用修正线性切线法控制动态物体的加速度

IF 0.5 4区数学

Proceedings of the Steklov Institute of Mathematics Pub Date : 2024-08-20 DOI: 10.1134/s0081543824030131

S. A. Reshmin, M. T. Bektybaeva

引用次数: 0

On the Problem of Optimal Stimulation of Demand 论最佳刺激需求问题

IF 0.5 4区数学

Proceedings of the Steklov Institute of Mathematics Pub Date : 2024-08-20 DOI: 10.1134/s0081543824030039

A. S. Aseev, S. P. Samsonov

引用次数: 0