The necessary optimality conditions for a nonlinear stationary system whose state functional is not differentiable with respect to the control

2010

Closed access Metadata (CSL-JSON)
DOI 10.3103/s1066369x10060046
Data confidence 70 medium
How this score is calculated

It is built from checkable properties of the record itself: whether the article has a DOI, how many independent sources confirmed its data, whether the required fields are filled in, and how recent the latest confirmation is. Disagreement between sources and a missing identifier lower it. A value of 80 or above means the record was published without further checking; 60 to 79 means it is published at reduced confidence, with a manual check advisable. A record verified by an editor by hand is never pushed below 90 by a recalculation. This scores our data about the article, not the article itself.

Abstract

We consider a control system described by a nonlinear elliptic equation. Its control-state mapping is extendedly differentiable but not Gateaux differentiable for large values of the domain dimension and the nonlinearity index. We obtain the necessary optimality condition for various state functionals.