Several transversality properties of pairs of sets and their role in the convergence analysis of fundamental projection algorithms will be discussed. Dual characterizations of the properties in terms of Fréchet, limiting and proximal normals will be provided. The new ‘intrinsic transversality’ property will be examined.
The talk is based on the following recent papers.
A. Y. Kruger and N. H. Thao, Regularity of collections of sets and convergence of inexact alternating projections, J. Convex Anal. 23 (2016), no. 3, 823–847.
A. Y. Kruger, D. R. Luke and N. H. Thao, Set regularities and feasibility problems, Math. Program., DOI 10.1007/s10107-016-1039-x.
A. Y. Kruger, D. R. Luke and N. H. Thao, About subtransversality of collections of sets, arXiv:1611.04787.
A. Y. Kruger, About intrinsic transversality of pairs of sets, arXiv:1701.08246.
The current work is supported by the Australian Research Council, project DP160100854.
Speaker: A/Prof. Alex Kruger (Centre for Informatics and Applied Optimization (CIAO), Federation University Australia)
Event website: www.rmitopt.org
About the speaker:
Alex Kruger received his PhD in mathematics from the Belarusian State University in 1981. Prior to joining University of Ballarat in 2003, he had worked at several universities and research institutions in Minsk, Belarus and also spent 4 months doing research as a Fulbright Scholar at Indiana University South Bend, USA. He has published about 85 papers in the fields of generalized differentiation, optimisation theory and variational analysis.
Currently Alex is Research Director of Centre for Informatics and Applied Optimization (CIAO) at Federation University Australia.
How to participate in this seminar:
1. Book your nearest ACE facility;
2. Notify Vera Roshchina at RMIT (rmitopt@rmit.edu.au) 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)