Electron. J. Diff. Equ., Vol. 2010(2010), No. 19, pp. 1-7.

Minimizing convex functions by continuous descent methods

Sergiu Aizicovici, Simeon Reich, Alexander J. Zaslavski

Abstract:
We study continuous descent methods for minimizing convex functions, defined on general Banach spaces, which are associated with an appropriate complete metric space of vector fields. We show that there exists an everywhere dense open set in this space of vector fields such that each of its elements generates strongly convergent trajectories.

Submitted June 27, 2009. Published January 28, 2010.
Math Subject Classifications: 37L99, 47J35, 49M99, 54E35, 54E50, 54E52, 90C25.
Key Words: Complete uniform space; convex function; descent method; initial value problem; minimization 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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