FIRST- AND SECOND-ORDER DIRECTIONAL DERIVATIVES OF A MAX-TYPE FUNCTION INDUCED FROM AN INEQUALITY STATE CONSTRAINT - Collections

＜journal article＞
FIRST- AND SECOND-ORDER DIRECTIONAL DERIVATIVES OF A MAX-TYPE FUNCTION INDUCED FROM AN INEQUALITY STATE CONSTRAINT

Creator	Author PID K000705 Creator Name Kawasaki, Hidefumi 川崎, 英文 Affiliation Affiliation Name Graduate School of Mathematics, Kyushu University 九州大学大学院数理学研究科
Language	English
Publisher	Research Association of Statistical Sciences
Publisher	統計科学研究会
Date	1997-03
Source Title	Bulletin of informatics and cybernetics
Vol	29
Issue	1
First Page	41
Last Page	49
Publication Type	Version of Record
Access Rights	open access
Crossref DOI	https://doi.org/10.5109/13460
Related DOI	Bulletin of informatics and cybernetics \|\| 29(1) \|\| p41-49
Related DOI	http://bic.math.kyushu-u.ac.jp/
Related URI	Bulletin of informatics and cybernetics \|\| 29(1) \|\| p41-49
Related URI	http://bic.math.kyushu-u.ac.jp/
Relation	Bulletin of informatics and cybernetics \|\| 29(1) \|\| p41-49
Relation	http://bic.math.kyushu-u.ac.jp/
Abstract	In this paper, we deal with a max-type function $ S(x) := mathrm{max}_{t in T} f(x(t), t) $, where $ x $ is a $ n $-dimensional vector-valued continuous functions. This max-type function is induced fr...om an inequality state constraint $ f(x(t), t) leqq 0 $, which appears in variational problems and optimal control problems. We give formulae for first- and second-order directional derivatives of $ S(x) $. We show that the one-side state constraint $ x(t) geqq a(t) $ always forms an envelope except two trivial cases.show more

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