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

川崎 英文

doi:10.5109/13460

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

DOI HANDLE 被引用文献1件オープンアクセス

川崎英文

九州大学大学院数理学研究科

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抄録

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 from 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.