On second-order epi-derivative in terms of ρ-hausdorff distance

Abstract EN

The second-order epi-derivatives plays an important role in nonsmooth analysis and in statements of optimality conditions.

Identifying functions with their epigraphs and subdifferentials operators with their graphs and using, as set convergence notion, the −Hausdorff distance convergence, we obtain in Banach spaces, some new relations between the second-order epi-derivative of convex function and proto-derivative of subdifferential operator, one also proves that the conjugate of second-order epi-derivative of convex function is the second-order epi-derivative of its conjugate function.

These results are extended of results introduced by Rockafellar in finite-dimensioal spaces.