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.

Publisher
Institute of Electrical and Electronics Engineers Inc.
Language
English
Pages
767-772
Status
Published
Number
8820515
Year
2019
Organizations
  • 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
Keywords
Efficiency; Functionals; Nonlinear compounds; Objective functions; Optimal control problem; Optimization method; Optimization problems; Search method; Unimodality; Optimal control systems
Date of creation
24.12.2019
Date of change
24.12.2019
Short link
https://repository.rudn.ru/en/records/article/record/55219/