March 29. Borwein participated in the Distinguished Lecturer Series in Mathematics and Applications at the University of South Australia, speaking on “Entropy and Projection Methods for Inverse Problems”. For details, see Announcement and Abstract.
Abstract: I shall discuss in “tutorial mode” the formalization of inverse problems such as signal recovery and option pricing; first as (convex and non-convex) optimization problems and second as feasibility problems — over the infinite dimensional space of signals. I shall touch on the following topics (more is an unrealistic task):
1. The impact of the choice of “entropy” (e.g., Boltzmann-Shannon,Burg entropy, Fisher information) on the well-posedness of the problem and the form of the solution.
2. Convex programming duality: what it is and what it buys you.
3. Algorithmic consequences.
4. Non-convex extensions: life is hard. But sometimes more works than should.