In this short note, we derive an upper estimate of Clarke's subdifferential marginal functions in Banach spaces. The structure the is very similar to other results already obtained literature. novelty lies on fact that our assertions general spaces, and avoid use Asplund assumption.

and Applied Analysis 3 Furthermore, if h is a convex function, then ∂ c h(?̂?) is in accordance with the subdifferential ∂h(?̂?) in convex analysis; that is,

We prove that the subdifferential of any semi-algebraic extended-real-valued function on Rn has n-dimensional graph. We discuss consequences for generic semi-algebraic optimization problems.

in this paper we study optimization problems with infinite many inequality constraints on a banach space where the objective function and the binding constraints are locally lipschitz‎. ‎necessary optimality conditions and regularity conditions are given‎. ‎our approach are based on the michel-penot subdifferential.

We apply nonsmooth analysis to a well known optical inverse problem, phase retrieval. The phase retrieval problem arises in many different modalities of electromagnetic imaging and has been studied in the optics literature for over forty years. The state of the art for this problem in two dimensions involves iterated projections for solving a nonconvex feasibility problem. Despite widespread us...