directional derivatives

On a class of nonsmooth composite functions

  • Alexander Shapiro
    • Categories Convex and Nonsmooth Optimization, Nonsmooth Optimization Tags , , , , ,

    We discuss in this paper a class of nonsmooth functions which can be represented, in a neighborhood of a considered point, as a composition of a positively homogeneous convex function and a smooth mapping which maps the considered point into the null vector. We argue that this is a sufficiently rich class of functions and … Read more

    On differentiability of symmetric matrix valued functions

  • Alexander Shapiro
    • Categories Convex and Nonsmooth Optimization Tags , , ,

    With every real valued function, of a real argument, can be associated a matrix function mapping a linear space of symmetric matrices into itself. In this paper we study directional differentiability properties of such matrix functions associated with directionally differentiable real valued functions. In particular, we show that matrix valued functions inherit semismooth properties of … Read more