Hoạt động trong tuần

Thời gian: từ 9h00 đến 11h00 sáng thứ 4 ngày 27.12.2023

Địa điểm: Phòng 302 nhà A5 Viện Toán học.

Tóm tắt: Given nonempty, closed and convex sets $C subset mathcal{H}$, $Q subset mathcal{K}$ in Hilbert spaces $mathcal{H}, mathcal{K}$ and a bounded linear operator $A : mathcal{H} to mathcal{K}$, the split feasibility problem (SFP) is to find $x in C$ such that $Ax in Q$. The problem was introduced by Censor and Elfving [Numer. Algorithms 1994] to model phase retrieval problems in signal processing. During the last three decades, many efforts have been made to design solution algorithms for SFP. Interestingly, this feasibility problem can be reformulated as a fixed point problem or a convex minimization one; hence, advanced tools from operator theory and optimization machinery can be fully exploited. In the first part of the talk, we will review some basic solution algorithms for SFP resulting from this approach, and then discuss further the gradient projection method with Polyak’s stepsize. The second part of the talk is about solution stability of SFP w.r.t. small changes of input data, where SFP is recast as a parametric generalized equation to which variational analysis techniques are applied. Finally, if time allows, we will address how SFP arises as a sub-problem in our recent algorithms for detecting singular points of linear discrete control systems with disturbances and of corresponding optimal control problems.