Theoretical fundamentals for unimodality estimation of an objective functional in the optimal control problem

The use of various optimization methods and the efficiency of their work strongly depends on the type of functional under investigation. It turned out that in the case of solving optimization problems with a nonlinear compound functional, it is not at all easy to estimate its convexity. And the absence of the unimodality property of the objective function means the instability and low efficiency of the application of gradient extremum search methods. This paper is devoted to the study of the properties of unimodality and convexity of functionals. The nontriviality of the problem of estimating the unimodality of a functional is shown, the concept of a fundamental sequence of functions that are the arguments of the objective functional is introduced, theorems on sufficient conditions for the absence of unimodality of the objective function are formulated and proved. © 2019 IEEE.

Авторы
Редакторы
-
Издательство
Institute of Electrical and Electronics Engineers Inc.
Номер выпуска
-
Язык
Английский
Страницы
767-772
Статус
Опубликовано
Подразделение
-
Ссылка
-
Номер
8820515
Том
-
Год
2019
Организации
  • 1 Federal Research Center Computer Science and Control, Russian Academy of Sciences, RUDN University, Moscow, Russian Federation
  • 2 Federal Research Center 'Computer Science and Control', Russian Academy of Sciences, Moscow, Russian Federation
Ключевые слова
Efficiency; Functionals; Nonlinear compounds; Objective functions; Optimal control problem; Optimization method; Optimization problems; Search method; Unimodality; Optimal control systems
Дата создания
24.12.2019
Дата изменения
24.12.2019
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/55219/