Necessary Second-Order Conditions for a Strong Local Minimum in a Problem with Endpoint and Control Constraints

Nikolai Pavlovich Osmolovskii ()
Additional contact information
Nikolai Pavlovich Osmolovskii: Polish Academy of Sciences

Journal of Optimization Theory and Applications, 2020, vol. 185, issue 1, No 1, 16 pages

Abstract: Abstract The method of sliding modes (relaxation) was originally invented in optimal control in order to give a transparent proof of the maximum principle (a first-order necessary condition for a strong local minimum) using the local maximum principle (a first-order necessary condition for a weak local minimum). In the present work, we use this method to derive second-order necessary conditions for a strong local minimum on the base of such conditions for a weak local minimum. For simplicity, we confine ourselves to the consideration of the Mayer problem with endpoint equality and inequality constraints and control inequality constraints given by a finite number of twice smooth functions. Assuming that the gradients of active control constraints are linearly independent, we provide a rather short proof of second-order necessary conditions for a strong local minimum.

Keywords: Weak minimum; Strong minimum; Pontryagin minimum principle; Critical cone; Quadratic form; 49K15 (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10957-020-01647-4 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:joptap:v:185:y:2020:i:1:d:10.1007_s10957-020-01647-4

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1007/s10957-020-01647-4

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

More articles in Journal of Optimization Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().