joint work with Boris Mordukhovich
We present a semismooth inverse mapping theorem for tilt-stable local minimizers of a function. Then we discuss a Newton method for a tilt-stable local minimum of an unconstrained optimization problem.
joint work with Helmut Gfrerer
The talk is devoted to a new notion of semismoothness which pertains both sets as well as multifunctions. In the case of single-valued maps it is closely related with the standard notion of semismoothness introduced by Qi and Sun in 1993. Semismoothness can be equivalently characterized in terms of regular, limiting and directional limiting coderivatives and seems to be the crucial tool in construction of Newton steps in case of generalized equations. Some basic classes of semismooth sets and mappings enabling us to create an elementary semismooth calculus will be provided.
joint work with Jiri Outrata
The talk deals with a semismooth Newton method for solving generalized equations (GEs), where the linearization concerns both the single-valued and the multi-valued part and it is performed on the basis of the respective coderivatives. Two conceptual algorithms will be presented and shown to converge locally superlinearly under relatively weak assumptions. Then the second one will be used in order to derive an implementable Newton-type method for a frequently arising class of GEs.