An extension of the Schwarzkopf multiplier rule in optimal control

• Type: Article in International Scientific Journal
• Date: 2011

Authors

Francis Clarke (Author) Other; Yuri Ledyaev (Author) Other; Maria do Rosário de Pinho (Author) FEUP

Journal

Title: SIAM Journal on Control and Optimization

Vol. 49 No. 2

Pages: 599-610

ISSN: 0363-0129

Publisher: Society for Industrial and Applied Mathematics

Indexing

ISI Web of Knowledge - 5 Citations

ISI Web of Science

Scopus - 5 Citations

INSPEC

Scientific classification

FOS: Engineering and technology > Electrical engineering, Electronic engineering, Information engineering

CORDIS: Physical sciences > Mathematics > Applied mathematics > Engineering mathematics

Other information

Authenticus ID: P-002-XM1

DOI: 10.1137/09078047x

Abstract (EN): The search for multiplier rules in dynamic optimization has been an important theme in the subject for over a century; it was central in the classical calculus of variations, and the Pontryagin maximum principle of optimal control theory is part of this quest. A more recent thread has involved problems with so-called mixed constraints involving the control and state variables jointly, a subject which now boasts a considerable literature. Recently, Clarke and de Pinho proved a general multiplier rule for such problems that extends and subsumes rather directly most of the available results, namely, those which postulate some kind of rank condition or, more generally, a constraint qualification (or generalized Mangasarian-Fromowitz condition). An exception to this approach is due to Schwarzkopf, whose well-known theorem replaces the rank hypothesis, for relaxed problems, by one of covering. The purpose of this article is to show how to obtain this type of theorem from the general multiplier rule of Clarke and de Pinho. In so doing, we subsume, extend, and correct the currently available versions of Schwarzkopf's result.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 12