Report Title：Equilibrium programming: background and some new concepts

Reporter：Boris Budak

Institution：Moscow State University

Time：November 17,2022  15:45-17:45,

Location：ZOOM ID：862 062 0549，Code：2022

Meeting link：//us02web.zoom.us/j/8620620549?pwd=bGhsaG15WjRza2V3ZEN4TzJYZ1FZQT09

Abstract：Equilibrium programming is a broad area of mathematics that studies mathematical models of numerous phenomena in natural sciences and economics. A typical situation is when exact values of functional Φ(v,w) are not available when finding the numerical solution to the  equilibrium programming problem and we have only their approximations. It is known that numerical models do not always work correctly in that situation, and different types of regularization must be applied. One of the best-known of these is Tikhonov’s regularization, which is usually used in processing approximate data. Some classic and new concepts of regularization will be discussed, a new regularized shooting model based on Tikhonov regularization for solving problems of equilibrium programming with inexact data will be given as an example.

Introduction of the Reporter：Boris Budak is an associated professor of Faculty of Computational Mathematics and Cybernetics, Moscow State University. His Main Scientific Interests and Results including:

1. Extremal problems with disturbed data, optimal control, stabilization and regularization.

2. Developed and investigated a family of continuous methods for equilibrium programming problems solving, developed regularized analogues of these methods for the situation, when initial data is disturbed.

3. Created a new so-called “shooting” method for equilibrium programming problems solving, developed regularized analogue of it.

4. Solved some problems dedicated to a search of an operator with minimal norm, that guarantees a given solution of a linear operator equation in Hilbert spaces.