4 papers · 1 filter
On the role of semismoothness in the implicit programming approach to selected nonsmooth optimization problems
Helmut Gfrerer, Michal Kočvara, Jiří V. Outrata
The paper deals with the implicit programming approach to a class of Mathematical Programs with Equilibrium Constraints (MPECs) and bilevel programs in the case when the correspond…
On strict proto-differentiability of set-valued mappings
Helmut Gfrerer
We will show that a multifunction is strictly proto-differentiable at a point of its graph if and only if it is graphically strictly differentiable, i.e., the graph of the multifun…
On second-order variational analysis of variational convexity of prox-regular functions
Helmut Gfrerer
Variational convexity, together with ist strong counterpart, of extended-real-valued functions has been recently introduced by Rockafellar. In this paper we present second-order ch…
On the role of semismoothness in nonsmooth numerical analysis: Theory
H. Gfrerer, J. V. Outrata
For the numerical solution of nonsmooth problems, sometimes it is not necessary that an exact subgradient/generalized Jacobian is at our disposal, but it suffices that a semismooth…