Browsing School of Arts and Sciences by Author "Nour, Chadi"

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Browsing School of Arts and Sciences by Author "Nour, Chadi"

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  • Nour, Chadi (2016-03-30)
    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.
  • Nour, Chadi; Stern, Ron J.; Takche, Jean (2016-04-08)
    We consider sets S С R satisfying a certain exterior sphere condition, and it is shown that under wedgedness of S, it coincides with φ-convexity. We also offer related improvements concerning the union of uniform closed ...
  • Nour, Chadi; Takche, Jean (2018-04-17)
    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.
  • Nour, Chadi (L' Universite Clause Bernard- Lyon 1, 2003-12-10)
    The main object of this thesis is the application of new methods from nonsmooth analysis and which use the Hamilton-Jacobi equation for the study of certain problems in control theory. There are three parts in our work: * ...
  • Nour, Chadi; Takche, Jean (2020-03-12)
    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 ...
  • Nour, Chadi (2018-04-18)
    We provide a sufficient condition for the proto-Lipschitz continuity of the state constrained bilateral minimal time function. Com- pared with the sufficient conditions given in [11], our new condition does not impose any ...
  • Chamoun, Samara; Nour, Chadi (2021-11-23)
    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 ...
  • Zeidan, Vera; Nour, Chadi; Saoud, Hassan (2021-11-24)
    For an optimal control problem governed by a controlled nonconvex sweeping process, we provide, using an exponential penalization technique, existence of solution and nonsmooth necessary conditions in the form of the ...
  • Nour, Chadi; Zeidan, Vera (2021-11-23)
    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 ...
  • Nour, Chadi; Takche, Jean (2016-03-30)
    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.
  • Nour, Chadi (2018-04-17)
    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 ...
  • Nour, Chadi; Saoud, Hassan; Tackche, Jean (2018-04-17)
  • Nour, Chadi; Stern, Ronald J. (2016-03-30)
    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, ...
  • Nour, Chadi (2016-03-30)
    We study the Hamilton-Jacobi equation of the minimal time function in a domain which contains the target set. We generalize the results of Clarke and Nour [J. Convex Anal., 2004], where the target set is taken to be a ...
  • Nour, Chadi (Springer, 2018-04-18)
    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 ...
  • Nour, Chadi; Stern, Ronald J.; Takche, Jean (2016-03-30)
    The exterior sphere condition is compared to proximal smoothness, and examples are provided, which show that the two properties are not necessarily equivalent. Then conditions are given under which equivalence holds, ...
  • Nour, Chadi; Stern, Ron J.; Takche, Jean (2016-03-30)

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