Abstract:
The classical inverse/implicit function theorems revolve around solving an equation in terms of a parameter and tell us when the solution mapping associated with this equation is a (differentiable) function with respect to the parameter.
Already in 1927 Hildebrandt and Graves observed that one can put aside differentiability obtaining however that the solution mapping is just Lipschitz continuous. The idea has evolved in subsequent extensions most known of which are various reincarnations of the Lyusternik-Graves theorem.
In the last several decades it has been widely accepted that in order to derive estimates for the solution mapping,
e.g. to put them in use for proving convergence of algorithms, it is sufficient to differentiate what you can and leave the rest as is, hoping that the resulting problem is easier to handle. More sophisticated results may be obtained by employing various forms of metric regularity, starting from abstract results on mappings acting in metric spaces and ending with applications to numerical analysis.
I will focus in particular on strong metric subregularity, a property which, put next to the [strong] metric regularity, turns out to be equally instrumental in applications.
About the speaker:
Asen Dontchev received successively M.Sc. (in 1971) and Ph.D. (in 1974) in Control Sciences from the Warsaw University of Technology. He became Doctor of Mathematical Sciences in 1987 and soon after that – full Professor. Currently he is Associate Editor at Mathematical Reviews, a division of the American Mathematical Society (since 1990) and Adjunct Professor at the University of Michigan (since 2000). From 2007 till 2009 Asen Dontchev served as a Program Director of the Analysis Program, DMS of the US National Science Foundation. Since 2009 Dontchev’s research has been funded by the National Science Foundation (USA). He has supervised 8 Ph.D. students.
Asen Dontchev has about 130 publications, including three books published by Springer, one of which was translated into Russian, and three textbooks. According to Google Scholar, his works have been cited more than 3700 times, and according to MathSciNet more than 1200 times by more than 500 authors (since 2000). He has served on editorial boards of SIAM Journal on Control and Optimization, SIAM Journal on Optimization (till 2009), Journal of Mathematical Analysis and Applications, Journal of Optimization Theory and Applications and many others.
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)