Abstract

We derive a formula for the proximal subdifferential of the bilateral minimal time function in the linear case. As a consequence, we prove some new regularity properties for this function, essentially, we provide suitable weak controllability assumption under which its epigraph is locally φ0-convex.

Author information

Contact details are reproduced from the original publication and may be historical.

Chadi Nour

Dept. of Computer Science and Mathematics, Lebanese American University, Byblos Campus -- P.O. Box 36, Byblos, Lebanon

cnour@lau.edu.lb

Keywords

  • Bilateral and unilateral minimal time function
  • linear control system
  • phi-convexity
  • proximal analysis
  • nonsmooth analysis

Suggested citation

C. Nour. “Proximal Subdifferential of the Bilateral Minimal Time Function and some Regularity Applications.” Journal of Convex Analysis 20 (2013), No. 4, 1095–1112.

Copyright Heldermann Verlag 2013