Mathematics of Computation and Optimisation
Special Interest Group of the AustMS
The registration for virtual ANZIAM2021 meeting is now open at
https://www.anziam.org.au/ANZIAM+Annual+Conference+2021
In addition to live-streamed formal talks, the conference will use a platform that will enable live informal interaction among the participants outside of the virtual lecture rooms and will feature a number of social online events. The full description of these events is still to appear.
SCHOOL OF MATHEMATICS AND APPLIED STATISTICS (SMAS),
UNIVERSITY OF WOLLONGONG, AUSTRALIA
An exciting PhD scholarship is available in the School of Mathematics and Applied Statistics (SMAS) at the University of Wollongong, South Western Sydney campus, in the area of Optimisation. The title of the project is Determining the Convergence Speed of Derivative-free Optimisation Algorithms. The UOW scholarship is $28,092AUD tax-free per year for
three years full-time. Tuition fees (for up to 4 years) will be waived. The successful applicant will have the opportunity to work with both Australian and international collaborators, and extra funding may be available for conference travel. Applications are invited from domestic and international students who are able to commence PhD studies at the University of Wollongong in 2021.
https://documents.uow.edu.au/content/groups/public/@web/@eis/documents/doc/uow261302.pdf
HOW TO APPLY
If you are interested in applying for this scholarship, please contact Dr Chayne Planiden via email: chayne@uow.edu.au. Applications must include CV detailing previous education experience and academic transcripts. It is expected that the successful applicant will be available to commence this scholarship by 31 October 2021. Applications close 30 November, 2020.
Title: Scaled Relative Graph: Nonexpansive operators via 2D Euclidean Geometry
Speaker: Ernest Ryu (Seoul National University)
Date and Time: November 25th, 2020, 17:00 AEDT (Register here for remote connection via Zoom)
Abstract: Many iterative methods in applied mathematics can be thought of as fixed-point iterations, and such algorithms are usually analyzed analytically, with inequalities. In this work, we present a geometric approach to analyzing contractive and nonexpansive fixed point iterations with a new tool called the scaled relative graph (SRG). The SRG provides a rigorous correspondence between nonlinear operators and subsets of the 2D plane. Under this framework, a geometric argument in the 2D plane becomes a rigorous proof of contractiveness of the corresponding operator.
Title: Local and Global Inverse and Implicit Function Theorems
Speaker: Aram Arutyunov (Moscow State University) & S.E. Zhukovskiy (V. A. Trapeznikov Institute of Control Sciences of RAS)
Date and Time: November 18th, 2020, 17:00 AEDT (Register here for remote connection via Zoom)
Abstract: In the talk, we present a local inverse function theorem on a cone in a neighbourhood of abnormal point. We present a global inverse function theorem in the form of theorem on trivial bundle, guaranteeing that if a smooth mapping of finite-dimensional spaces is uniformly nonsingular, then it has a smooth right inverse satisfying a priori estimate. We also present a global implicit function theorem guaranteeing the existence and continuity of a global implicit function under the condition that the mappings in question are uniformly nonsingular. The generalization of these results to the case of mappings of Hilbert spaces and Banach spaces are discussed.