Iterative methods for nonlinear optimisation problems - Prospects and applications

Abstract: An important class of extremal problems in nonlinear functional analysis is the nonlinear optimisation problem where some of the objective functions are nonlinear. In many cases where existence of solutions is guaranteed, these solutions are not usually affordable in a direct way. Iterative methods (or algorithms), therefore provide a convenient way of approximating these solutions. To a large extent, most of these iterative methods can be traced to the popular gradient descent algorithm. This talk presents the prospects that may result in using a different approach, and its usefulness even to equivalent reformulations of the nonlinear optimisation problem. Its applicability in some areas of science and technology is highlighted and a spectacular application in radiotherapy treatment planning where algorithmic efficiency is especially required is demonstrated.

This work is Joint with Charles Ejike Chidume.

analysis of PDEsclassical analysis and ODEs

Audience: researchers in the topic

HA-GMT-PDE Seminar

Series comments: Description: A senior graduate student/postdoc series in harmonic analysis, geometric measure theory, and partial differential equations.

Meetings will be weekly, and usually will occur on Monday, with some exceptions. For each talk, the Zoom link is made available in the website too. Contact Bruno Poggi at poggi008@umn.edu if you would like to subscribe to the seminar mailing list.