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.

In this paper we study the mathematical program with geometric constraints such that the image of a mapping from a Banach space is included in a nonempty and closed subset of a finite dimensional space. We obtain the nonsmooth enhanced Fritz John necessary optimality conditions in terms of the approximate subdifferential. In the case where the Banach space is a weakly compactly generated Asplun...