The first RMITOpt talk next year will be on Friday 20 January, 12:30pm, by Prof. Asen Dontchev.
Speaker: Prof. Asen L. Dontchev, Mathematical Reviews and the University of Michigan
Title: Strong Metric Subregularity
Date and time: Friday, 20 January 2017, 12:30-13:30pm
Location: 8.9.66 (RMIT Access grid room)
Abstract: Although the property of strong metric subregularity of set-valued mappings has been present in the literature under various names and with various (equivalent) definitions for more than two decades, it has attracted much less attention than its older “siblings”, the metric regularity and the strong metric regularity.
In this talk I will try to show that the strong metric subregularity shares the main features of these two most popular regularity properties and is not less instrumental in applications. In particular, it obeys the inverse function theorem paradigm also for nonsmooth perturbations.
A sufficient condition for strong metric subregularity is established in terms of surjectivity of the Fréchet coderivative will be presented, and it will be shown by a counterexample that surjectivity of the limiting coderivative is not a sufficient condition for this property, in general. Then various versions of Newton’s method for solving variational inequalities will be considered including inexact and semismooth methods. A characterization of the strong metric subregularity of the KKT mapping will be demonstrated, as well as a radius theorem for the optimality mapping of a nonlinear programming problem. Finally, an error estimate is derived for a discrete approximation in optimal control under strong metric subregularity of the mapping involved in the Pontryagin principle.
Bio: Asen got both his MS and PhD degrees at Warsaw Polytechnics, Poland, in then famous Polish school in control. Then he moved to his home country, Bulgaria, where is received his DSc dgree, went through the ranks and became Full Professor at the Institute of Mathematics, Bulgarian Acad. of Sciences. In early 90s he accepted the position of Associate Editor at Mathematical Review in Ann Arbor, where he also has taught at the University of Michigan; he is currently appointed there as a Research Scientist. His research interests cover several areas in control, optimization, and applied analysis.