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Browsing by Author "Nour, C."

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Browsing by Author "Nour, C."

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  • The Bilateral Minimal Time Function 
    Nour, C. (2016-03-30)
    We study the minimal time function as a function of two variables (the initial and the terminal points). This function, called the "bilateral minimal time function", plays a central role in the study of the Hamilton-Jacobi ...
  • Existence of solutions to a global eikonal equation 
    Nour, C. (2016-03-30)
    We derive a geometric necessary and sufficient condition for the existence of solutions to a global eikonal equation. We also study the existence of a minimal solution to this equation, and its relation with the well-known ...
  • The Hamilton-Jacobi equation of minimal time control 
    Clarke, F. H.; Nour, C. (2018-04-17)
    We study the solutions of the Hamilton-Jacobi equation that arise in connection with minimal time control, in a new global framework. These solutions, for which we establish existence using the minimal time function as a ...
  • Nonconvex Duality in Optimal Control 
    Clarcke, F. H.; Nour, C. (2016-03-30)
    We derive a representation of the minimum cost of an optimal control problem in terms of the upper envelope of generalized semisolutions of the Hamilton--Jacobi equation.
  • Proximal Smoothness and the Exterior Sphere Condition 
    Nour, C.; Stern, R. J.; Takche, J. (2016-03-30)
    Proximal smoothness and the exterior sphere condition are compared. It is shown via examples that these two properties are not necessarily equivalent, and geometric conditions are provided under which the equivalence holds.
  • Regularity of the state constrained minimal time function 
    Nour, C.; Stern, R. J. (2016-03-30)
    The regularity of the state constrained minimal time function is studied. We generalize [P. Wolenski, Y. Zhuang, Proximal analysis and the minimal time function, SIAM J. Control Optim. 36 (1998) 1048–1072, Theorem 6.1] in ...
  • The state constrained bilateral minimal time function 
    Nour, C.; Stern, R.J. (2018-04-17)
    We generalize, to the bilateral case (that is, with variable initial and end points), the main results of Nour and Stern [C. Nour, R.J. Stern, Regularity of the state constrained minimal time function, Nonlinear Anal. 66 ...
  • The θ-exterior sphere condition, φ-convexity, and local semiconcavity 
    Nour, C.; Stern, R. J.; Takche, J. (2016-04-08)
    We consider sets S⊂Rn satisfying a locally uniform exterior sphere condition called the θ-exterior sphere condition . It is shown that under wedgedness of S, this coincides with the φ-convexity property studied by Colombo ...