Abstract:
In post-optimal analysis and in the treatment of the so-called equilibrium constraints one often needs to analyze local stability of the solution maps which assign to some parameters (e.g. problem data) the respective solutions (optima or equilibria). One of the most important local stability notions is the Aubin (Lipschitz-like) property which ensures that the perturbed problems:
(i) do possess a solution, and
(ii) the distance of this solution from the original (reference) solution is bounded above by a multiple of the norm of the perturbation.
In the lecture, a new non-restrictive sufficient condition for the Aubin property will be presented in the general framework of implicitly defined multifunctions. In this development our main tools are generalized derivatives and coderivatives which provide a convenient description of the local behavior of nonsmooth and set-valued mappings. In particular, it is the directional limiting coderivative due to Helmut Gfrerer, which is tailored to fine local analysis of multifunctions along specified directions.
This new condition will then be specialized to constraint and variational systems having a frequently arising structure, which requires a development of a certain calculus for the directional limiting coderivatives. We will present one rule of this new calculus generalizing a formula due to Dontchev and Rockafellar. The advantages of this new approach will be illustrated by examples.
The lecture is based on a joint work with Helmut Gfrerer (Johannes Kepler Universität Linz).
About the speaker:
Professor Jiří Outrata is Senior Researcher in the Institute of Information Theory and Automation of the Czech Academy of Sciences in the Czech Republic. In the period 1991-2001 he spent several years in Germany on leave with the University of Bayreuth and the University of Erlangen-Nuremberg. His technical background is optimal control but, since 1993 his main attention is devoted to mathematical programs with equilibrium constraints.
In 2007 Jiří Outrata was awarded the Honorary Medal of Bernard Bolzano and since 2013 he has been an Adjunct Professor of the Federation University Australia.
Venue:
ACE room T121, T Building, Mt Helen Campus, Federation University Australia
How to participate in this seminar:
1. Book your nearest ACE facility;
2. Notify the seminar convenor at Federation University (Helen Wade) to notify you will be participating.
No access to an ACE facility? Contact Maaike Wienk to arrange a temporary Visimeet licence for remote access (limited number of licences available – first come first serve)