Infimal Convolution and Optimal Time Control Problem II: Limiting Subdifferential

Grigorii Ivanov (1) , Lionel Thibault (2)

1 MIPT - Moscow Institute of Physics and Technology [Moscow]
2 IMAG - Institut Montpelliérain Alexander Grothendieck

This paper is the continuation of our study of a general minimal time problem with a convex constant dynamics and a lower semicontinuous extended real-valued target function defined on a Banach space. We study several properties of the limiting subdifferential for the infimum time function and we provide explicit expressions of the limiting subdifferential. Necessary and sufficient conditions for the infimum time function to be lower regular are presented. The sharpness of assumptions is shown through diverse examples.

Mots clés: Fréchet subdifferential; Mordukhovich limiting subdifferential; Minimal time function; Minimal time projection; Infimal convolution; Lower regular function

Domaines: Mathématiques [math]

Grigorii Ivanov, Lionel Thibault. Infimal Convolution and Optimal Time Control Problem II: Limiting Subdifferential. Set-Valued and Variational Analysis, 2017, 25 (3), pp.517-542. ⟨10.1007/s11228-017-0402-2⟩. ⟨hal-02072730⟩