Electron. J. Diff. Eqns., Vol. 2003(2003), No. 24, pp. 1-11.

Two convergence results for continuous descent methods

Simeon Reich & Alexander J. Zaslavski

Abstract:
We consider continuous descent methods for the minimization of convex functionals defined on general Banach space. We establish two convergence results for methods which are generated 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 August 5, 2002. Published March 10, 2003.
Math Subject Classifications: 37L99, 47J35, 49M99, 54E50, 54E52, 90C25.
Key Words: Complete metric space, convex function, descent method, porous set, regular vector field

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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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