A controlled sweeping process with prox-regular set, W1,2-controls, and separable endpoints constraints is considered in this paper. Existence of optimal solutions is established and local optimality conditions are derived ...

We generalize a recent result of C. Nour, H. Saoud and J. Takche [Regularization via sets satisfying the interior sphere condition, J. Convex Analysis 25(1) (2018) 1--19], where the authors provided an inner approximation ...

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 ...

We extend to C×W1,2 -local minimizers and nonautonomous perturbation function, the necessary optimality conditions derived in [1], via continuous-time approximations, for W1,2×W1,2 -local minimizers of an optimal control ...

We provide a new analytical proof for a strengthened version of the variable radius form of the union of closed balls conjecture. We also introduce a strong version of this conjecture and discuss its validity.

The Pontryagin-type maximum principle derived in [30] for optimal control problems involving sweeping processes is generalized to the case where the sweeping set C is nonsmooth and not necessarily bounded, namely, C is the ...

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, ...