TY - JOUR

T1 - Exact penalty functions for optimal control problems I

T2 - Main theorem and free-endpoint problems

AU - Dolgopolik, M. V.

AU - Fominyh, A. V.

PY - 2019/11/1

Y1 - 2019/11/1

N2 - In this two-part study, we develop a general approach to the design and analysis of exact penalty functions for various optimal control problems, including problems with terminal and state constraints, problems involving differential inclusions, and optimal control problems for linear evolution equations. This approach allows one to simplify an optimal control problem by removing some (or all) constraints of this problem with the use of an exact penalty function, thus allowing one to reduce optimal control problems to equivalent variational problems and apply numerical methods for solving, eg, problems without state constraints, to problems including such constraints, etc. In the first part of our study, we strengthen some existing results on exact penalty functions for optimisation problems in infinite dimensional spaces and utilise them to study exact penalty functions for free-endpoint optimal control problems, which reduce these problems to equivalent variational ones. We also prove several auxiliary results on integral functionals and Nemytskii operators that are helpful for verifying the assumptions under which the proposed penalty functions are exact.

AB - In this two-part study, we develop a general approach to the design and analysis of exact penalty functions for various optimal control problems, including problems with terminal and state constraints, problems involving differential inclusions, and optimal control problems for linear evolution equations. This approach allows one to simplify an optimal control problem by removing some (or all) constraints of this problem with the use of an exact penalty function, thus allowing one to reduce optimal control problems to equivalent variational problems and apply numerical methods for solving, eg, problems without state constraints, to problems including such constraints, etc. In the first part of our study, we strengthen some existing results on exact penalty functions for optimisation problems in infinite dimensional spaces and utilise them to study exact penalty functions for free-endpoint optimal control problems, which reduce these problems to equivalent variational ones. We also prove several auxiliary results on integral functionals and Nemytskii operators that are helpful for verifying the assumptions under which the proposed penalty functions are exact.

KW - differential inclusion

KW - exact penalty function

KW - free-endpoint problem

KW - optimal control

UR - http://www.scopus.com/inward/record.url?scp=85070103585&partnerID=8YFLogxK

U2 - 10.1002/oca.2530

DO - 10.1002/oca.2530

M3 - статья

AN - SCOPUS:85070103585

VL - 40

SP - 1018

EP - 1044

JO - Optimal Control Applications and Methods

JF - Optimal Control Applications and Methods

SN - 0143-2087

IS - 6

ER -