Convergence of the Gradient Method in Normed Linear Spaces.
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WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER
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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 Currys 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 Currys 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.
- Theoretical Mathematics