Лекция профессора Андреаса Фишера (Дрезден, Германия)

28 мая 2013 г., 15:00, в ауд. 612 2-го учебного корпуса состоится лекция Андреаса Фишера, профессора, директора Института вычислительной математики Технического Университета Дрездена.

Author: Prof. Dr. Andreas Fischer

Title: A Framework for Smooth and Nonsmooth Equations with Nonisolated Solutions

Abstract:

Systems of equations with nonisolated solutions arise in several applications, for example one can think of nonunique multipliers in Karush-Kuhn-Tucker conditions, multiobjective optimization, or generalized Nash equilibrium problems. The nonisolatedness of solutions implies difficulties for the fast local convergence of algorithms. For example, for a smooth system of equations, its Jacobian at a nonisolated solution is singular so that Newton's method may fail to converge. The talk will highlight developments to overcome those difficulties. We will discuss the role of error bounds and related conditions to substitute nonsingularity assumptions. Furthermore, we will show algorithmic concepts by which superlinear convergence to a nonisolated solution can be achieved. In particular, a local framework for dealing with nonsmooth systems of equations with possibly nonisolated solutions will be presented.

Affiliations:

Prof. Dr. Andreas Fischer
Director of the Institute of Numerical Mathematics
Technische Universität Dresden
Faculty of Mathematics and Natural Sciences
Institute of Numerical Mathematics
01062 Dresden
phone: +49 (351) 463-34148
fax: +49 (351) 463-34268
email: Andreas.Fischer@tu-dresden.de