Variational Analysis for the Bilateral Minimal Time Function

2017/05/09 by Nguyen, Luong V.
#FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.1705.03249

Abstract

In this paper, we derive formulas for the Fréchet (singular) subdiferentials of the bilateral minimal time function T:ℝⁿ × ℝⁿ → [0,+∞] associated with a system governed by differential inclusions. As a consequence, we give a connection between the Fréchet normals to the sub-level sets of T and to its epigraph. Finally, we show that the Fréchet normal cones to the sub-level set of T at a point (α,β) and to epi(T) at ((α,β),T(α,β)) have the same dimension.

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