Applied Analysis Seminar
Tuesday July 9 in K9509, SFU
Speaker and Title:
2:00 - 2:45: Philip Loewen (UBC, Mathematics) "Smooth Bumps and Their Gradients"Abstract:
A bump is a real-valued function whose support is nonempty and bounded; continuously differentiable bumps are called smooth.In this talk I will outline the results of recent investigations (joint with J. Borwein, I. Kortezov, and M. Fabian) into the kinds of sets obtainable as the range of the gradient for a smooth bump. I will show how to build a smooth bump on the plane whose gradient range is not simply connected. Passing to infinite dimensional Banach spaces, I will explain how to use a given smooth bump to build another one whose gradient range exactly reproduces the closure of a preassigned convex neighbourhood of the origin; the same procedure covers other reasonable shapes. Some tantalizing open problems that motivated this research remain unsolved: I'll mention one of these and its current status.
Speaker and Title:
2:45 - 3:30: Jon Borwein (CECM) "Bregman Monotone Optimization Algorithms"Abstract:
The notions of Bregman distance and ofBregman monotonicity provide a unified way of analysing many non-linear iterative methods for reconstruction and feasibility problems.I shall survey my recent work on this subject with Heinz Bauschke and Patrick Combettes. I'll also describe some related work on barrier functions with Jon Vanderwerff.