Electron. J. Diff. Eqns., Vol. 2004(2004), No. 45, pp. 1-13.

Convergence results for a class of abstract continuous descent methods

Sergiu Aizicovici, Simeon Reich, & Alexander J. Zaslavski

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 $\sigma$-porous, we conclude that our results apply to most vector fields in the sense of Baire's categories.

Submitted January 7, 2004. Published March 30, 2004.
Math Subject Classifications: 37L99, 47J35, 49M99, 54E35, 54E50, 54E52, 90C25.
Key Words: Complete metric space, descent method, Lipschitzian function, porous set, regular vector field.

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Sergiu Aizicovici
Department of Mathematics, Ohio University
Athens, OH 45701-2979, USA
email: aizicovi@math.ohiou.edu
Simeon Reich
Department of Mathematics
The Technion-Israel Institute of Technology
32000 Haifa, Israel
email: sreich@tx.technion.ac.il
Alexander J. Zaslavski
Department of Mathematics
The Technion-Israel Institute of Technology
32000 Haifa, Israel
email: ajzasl@tx.technion.ac.il

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