Organizer: Zev Woodstock

Wednesday, April 24, SAS 4201, 12:15 – 13:15

Speaker: Farid Benmouffok
Title: Interesting problems in functional analysis

Abstract: An outdoor discussion on some analysis problems.

Wednesday, April 17, SAS 4201, 12:15 – 13:15

Speaker: Zev Woodstock
Title: Proximal methods in optimization

Abstract: I will give a brief introduction to proximal methods, when to use them, what they do, and the analysis behind what makes them work.

Wednesday, April 10, SAS 4201, 12:15 – 13:15

Speaker: Steven Gilmore
Title: A debt management problem with bankruptcy risk and currency devaluation.

Abstract: A problem of optimal debt management is modeled as an interaction between a sovereign state and a pool of investors, in infinite time horizon with exponential discount and a bankruptcy risk. At each time, the government decides which fraction of the gross domestic product must be used to repay the debt, and how much to devaluate its currency. Both of these options reduce the debt but have a social cost. In this talk, we explore the derivation of the model and past results; the existence of an equilibrium solution is obtained by a topological argument.

Wednesday, April 03, SAS 4201, 12:15 – 13:15

Speaker: Prerona Dutta
Title: Upper estimate for covering number of the class of generalized bounded variation functions.

Abstract: In this talk we will provide an upper estimate for a minimal number of functions needed to present all bounded generalized variation functions upto an accuracy of epsilon (>0) with respect to L^1 (R)- distance.

Wednesday, February 27, SAS 4201, 14:00 – 15:00

Speaker: Ben Freedman
Title: Nonlinearly perturbed Legendre differential equations

Abstract: In this talk, we consider nonlinearly perturbed Legendre differential equations subject to the usual boundary conditions. For such problems we establish sufficient conditions for the existence of solutions and in some cases we provide a qualitative description of solutions depending on a parameter. The results presented depend on the size and limiting behavior of the nonlinearities. In the case of weakly nonlinear problems, our results rely on a nonstandard application of the implicit function theorem.

Wednesday, February 13, SAS 4201, 14:00 – 15:00

Speaker: None (Discussion session)
Title: Exercises and Problems day.

Wednesday, February 06, SAS 4201, 14:00 – 15:00

Speaker: None (Discussion session)
Title: A famous counterexample about the Alternating Projection algorithm.

Abstract: This paper proves that the method of alternating projections between two closed convex intersecting sets does not always converge in norm. Weak convergence was established by Bregman
(Soviet Math. Dokl. 6 (1965) 688), but the status of norm convergence was undetermined. An explicit counterexample is provided.

Wednesday, January 30, SAS 4201, 14:00 – 15:00

Speaker: Farid Benmouffok
Title: Connecting analysis and statistics.

Abstract: In this talk, we consider the link between some results in analysis and statistics. In particular, we discuss the group lasso penalization and its applications.

Wednesday, January 16, SAS 4201, 14:00 – 15:00

Speaker: Minh Bui
Title: On sums and convex combinations of projectors onto convex sets.

Abstract: The projector onto the Minkowski sum of closed convex sets is generally not equal to the sum of individual projectors. In this talk, we provide a complete answer to the question of characterizing the instances where such an equality holds. Our results unify and extend the case of linear subspaces and Zarantonello’s results for projectors onto cones. The question ”When is a convex average of projectors is a projector?” is also
discussed. In addition, we present the partial sum property for projectors onto convex cones as well as the univariate case.