We give a new and simple proof to the main result of [8] in which we derived a geometric necessary and sufficient condition for the existence ofsolutions to a global eikonal equation.

For a given multifunction, we provide proximal differentiability condition under which the equivalence between the interior sphere condition of each value of the multifunction and the interior sphere condition of its graph holds.

Let A ⊂ R n be a closed set and let S ⊂ R n be a set containing A. In this paper we study a new regularity class for A, called S-convexity, introduced by C. Nour, H. Saoud and J. Takche [Regularization via sets satisfying ...

For a nonlinear control system, we derive a ϕ0-convexity result for the epigraph of the bilateral minimal time function. This extends the main result in a previous publication of the second author [Proximal subdifferential ...

A numerical method and the theory leading to its success are developed in this letter to solve nonstandard optimal control problems involving sweeping processes, in which the sweeping set C is non-convex and coincides with ...

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 ...

For a linear control system, we provide conditions under which the bilateral minimal time function T(⋅,⋅) is semiconcave near a given point (α,β). A semiconvexity result of Nour [C. Nour, The bilateral minimal time function, ...

The main result of this paper contains a representation of the minimum cost of a free time control problem in terms of the upper envelope of generalized semisolutions of the Hamilton-Jacobi equation. A corollary generalizes ...