Electron. J. Diff. Eqns., Vol. 2007(2007), No. 31, pp. 1-6.

Stability of convergent continuous descent methods

Sergiu Aizicovici, Simeon Reich, Alexander J. Zaslavski

Abstract:
We consider continuous descent methods for the minimization of convex functions defined on a general Banach space. In our previous work we showed that most of them (in the sense of Baire category) converged. In the present paper we show that convergent continuous descent methods are stable under small perturbations.

Submitted September 3, 2006. Published February 22, 2007.
Math Subject Classifications: 37L99, 47J35, 49M99, 54E35, 54E50, 54E52, 90C25.
Key Words: Complete uniform space; convex function; descent method; generic property; initial value problem.

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Sergiu Aizicovici
Department of Mathematics, Ohio University
Athens, OH 45701, 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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