# Application of the hypodifferential descent method to the problem of constructing an optimal control

Research output

5 Citations (Scopus)

### Abstract

In this paper the problem of optimal control of a nonlinear ODE system with given boundary conditions and the integral restriction on control is considered. With the help of the theory of exact penalty functions the original problem is reduced to the problem of unconstrained minimization of a nonsmooth functional. The necessary minimum conditions in terms of hypodifferentials are found. A class of problems for which these conditions are also sufficient is distinguished. On the basis of these conditions the hypodifferential descent method is applied to the considered problem. Under some additional assumptions the hypodifferential descent method converges in a certain sense.

Original language English 1825-1839 15 Optimization Letters 12 8 Published - 1 Dec 2018

### Fingerprint

Descent Method
Optimal Control
Exact Penalty Function
Nonlinear ODE
Unconstrained Minimization
Sufficient
Restriction
Converge
Boundary conditions
Necessary

### Scopus subject areas

• Control and Optimization

### Cite this

@article{05d31a3984ca42db9ee76518b5c518e7,
title = "Application of the hypodifferential descent method to the problem of constructing an optimal control",
abstract = "In this paper the problem of optimal control of a nonlinear ODE system with given boundary conditions and the integral restriction on control is considered. With the help of the theory of exact penalty functions the original problem is reduced to the problem of unconstrained minimization of a nonsmooth functional. The necessary minimum conditions in terms of hypodifferentials are found. A class of problems for which these conditions are also sufficient is distinguished. On the basis of these conditions the hypodifferential descent method is applied to the considered problem. Under some additional assumptions the hypodifferential descent method converges in a certain sense.",
keywords = "Exact penalty function, Hypodifferential descent method, Nonsmooth functional, Optimal control, Variational problem, CONSTRAINTS",
author = "Fominyh, {A. V.} and Karelin, {V. V.} and Polyakova, {L. N.}",
year = "2018",
month = "12",
day = "1",
doi = "10.1007/s11590-017-1222-x",
language = "Английский",
volume = "12",
pages = "1825--1839",
journal = "Optimization Letters",
issn = "1862-4472",
publisher = "Springer",
number = "8",

}

In: Optimization Letters, Vol. 12, No. 8, 01.12.2018, p. 1825-1839.

Research output

TY - JOUR

T1 - Application of the hypodifferential descent method to the problem of constructing an optimal control

AU - Fominyh, A. V.

AU - Karelin, V. V.

AU - Polyakova, L. N.

PY - 2018/12/1

Y1 - 2018/12/1

N2 - In this paper the problem of optimal control of a nonlinear ODE system with given boundary conditions and the integral restriction on control is considered. With the help of the theory of exact penalty functions the original problem is reduced to the problem of unconstrained minimization of a nonsmooth functional. The necessary minimum conditions in terms of hypodifferentials are found. A class of problems for which these conditions are also sufficient is distinguished. On the basis of these conditions the hypodifferential descent method is applied to the considered problem. Under some additional assumptions the hypodifferential descent method converges in a certain sense.

AB - In this paper the problem of optimal control of a nonlinear ODE system with given boundary conditions and the integral restriction on control is considered. With the help of the theory of exact penalty functions the original problem is reduced to the problem of unconstrained minimization of a nonsmooth functional. The necessary minimum conditions in terms of hypodifferentials are found. A class of problems for which these conditions are also sufficient is distinguished. On the basis of these conditions the hypodifferential descent method is applied to the considered problem. Under some additional assumptions the hypodifferential descent method converges in a certain sense.

KW - Exact penalty function

KW - Hypodifferential descent method

KW - Nonsmooth functional

KW - Optimal control

KW - Variational problem

KW - CONSTRAINTS

UR - http://www.mendeley.com/research/application-hypodifferential-descent-method-problem-constructing-optimal-control

U2 - 10.1007/s11590-017-1222-x

DO - 10.1007/s11590-017-1222-x

M3 - статья

AN - SCOPUS:85035112181

VL - 12

SP - 1825

EP - 1839

JO - Optimization Letters

JF - Optimization Letters

SN - 1862-4472

IS - 8

ER -