11 citations · 20 across the 11 of their papers we have counts for
12 papers
Spherically Supported Sets with Variable Radii
Chadi Nour
We study closed sets for which, at every boundary point, there exists a containing supporting ball whose prescribed radius may vary from point to point. This extends the notion of…
Optimal Control of Sweeping Processes with Nonsmooth Moving Sets: A Numerical Algorithm
Chadi Nour
This paper extends the numerical method introduced by de Pinho et al. [22] and later developed in Nour and Zeidan [33, 37] to the nonautonomous case where the nonsmooth sweeping se…
Validity of the Strong Version of the Union of Uniform Closed Balls Conjecture in the Plane
Chadi Nour, Jean Takche
We prove the validity of the strong version of the union of uniform closed balls conjecture, formulated in 2011 as [4, Conjecture 2.5], in the plane.
Spherically Supported Property and the Exterior Sphere Condition with Infinite Radius
Chadi Nour
We present several new characterizations of the spherically supported geometric property introduced in [19], emphasizing its connection with the exterior sphere condition with infi…
New Characterizations of Strong Convexity
Chadi Nour, Jean Takche
Parallel to the main results of [13] and [14], which explore the equivalence between prox-regularity, the exterior sphere condition, and -convexity, we present novel characteriz…
The Complement of a Closed Set Satisfying the Extended Exterior Sphere Condition
Chadi Nour, Jean Takche
We provide a novel analytical proof of an improved version of [10, Theorem 3.1], showing that the complement of a closed set satisfying the extended exterior sphere condition is no…
The Variable Radius Form of the Extended Exterior Sphere Condition
Chadi Nour, Jean Takche
We introduce a variable radius form of the extended exterior sphere condition of [16], and then, we prove that the complement of a closed set satisfying this new property is nothin…
Numerical Method for a Controlled Sweeping Process with Nonsmooth Sweeping Set
Chadi Nour, Vera Zeidan
The numerical method developed in [30] for optimal control problems involving sweeping processes with smooth sweeping set C is generalized to the case where C is nonsmooth, namely,…
Nonsmooth optimality criterion for a -controlled sweeping process: Nonautonomous perturbation
Chadi Nour, Vera Zeidan
We extend to -local minimizers and nonautonomous perturbation function, the necessary optimality conditions derived in [1], via continuous-time a…
Pontryagin-type maximum principle for a controlled sweeping process with nonsmooth and unbounded sweeping set
Chadi Nour, Vera Zeidan
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…
The Extended Exterior Sphere Condition
Chadi Nour, Jean Takche
We prove that the complement of a closed set S satisfying an extended exterior sphere condition is nothing but the union of closed balls with common radius. This generalizes [11, T…
A Control Space Ensuring the Strong Convergence of Continuous Approximation for a Controlled Sweeping Process
Chadi Nour, Vera Zeidan
A controlled sweeping process with prox-regular set, -controls, and separable endpoints constraints is considered in this paper. Existence of optimal solutions is establis…