Convergence of the Gradient Method in Normed Linear Spaces.
Abstract
Recently Golomb and Tapia defined the gradient of a (C sup 1) functional on an arbitrary normed linear space. They showed that their gradient method coincides with the known method of steepest descent and established Curry's theorem (any cluster point of the gradient sequence is a stationary point) under the assumption that the gradient operator be single valued and continuous. In this paper the authors prove Curry's theorem in the full generality of normed linear spaces. This includes many important applications in which the gradient operator is neither continuous nor single valued.
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 01, 1974
- Accession Number
- ADA001653
Entities
People
- R. A. Tapia
- R. H. Byrd
Organizations
- University of Wisconsin–Madison