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 |
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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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