Convergence results for a class of abstract continuous descent methods
Date
2004-03-30
Authors
Aizicovici, Sergiu
Reich, Simeon
Zaslavski, Alexander J.
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
Abstract
We study continuous descent methods for the minimization of Lipschitzian functions defined on a general Banach space. We establish convergence theorems for those methods which are generated by approximate solutions to evolution equations governed by regular vector fields. Since the complement of the set of regular vector fields is σ-porous, we conclude that our results apply to most vector fields in the sense of Baire's categories.
Description
Keywords
Complete metric space, Descent method, Lipschitzian function, Porous set, Regular vector field
Citation
Aizicovici, S., Reich, S., & Zaslavski, A. J. (2004). Convergence results for a class of abstract continuous descent methods. <i>Electronic Journal of Differential Equations, 2004</i>(45), pp. 1-13.
Rights
Attribution 4.0 International