Extragradient Method for Finding a Saddle Point in a Multicriteria Problem with Dynamics

被引：0

作者：

Vasil'ev, F. P. ^{[1
]}

Antipin, A. S. ^{[2
]}

Artem'eva, L. A. ^{[1
]}

机构：

[1] Moscow MV Lomonosov State Univ, Fac Computat Math & Cybernet, Moscow 119991, Russia

[2] Russian Acad Sci, Dorodnitsyn Comp Ctr, Moscow 119333, Russia

来源：

PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS | 2017年 / 297卷

基金：

俄罗斯基础研究基金会;

关键词：

optimal control problem; Cauchy problem; multicriteria problem; saddle point; convergence;

D O I：

10.1134/S0081543817050224

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider an optimal control problem for a linear system of ordinary differential equations with an implicitly given boundary condition connected with a multicriteria problem. Such problems arise, for example, in the study of controlled objects that lose their stability under the influence of external perturbations, where it is required to return an object to stability by means of an appropriate choice of the control. We describe a possible mathematical model of this kind, propose an extragradient method for recovering the stability, and investigate its convergence.

引用

页码：S203 / S210

页数：8

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