The Gradient Projection Method and Curry's Theorem.

Abstract

Consider the sequence obtained by applying the gradient projection method to the problem of minimizing a continuously differentiable functional over a closed convex subset of a real Hilbert space. In this paper it is shown that if the subset is a regular subset, which includes polyhedral subsets, or the positive cone of an orthogonal set, then any cluster point of this sequence must be a constrained stationary point. These results generalize a well-known theorem, due to Curry, for unconstrained minimization in Euclidean space. (Author)

Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1970
Accession Number
AD0728447

Entities

People

  • G. P. Mccormick
  • R. A. Tapia

Organizations

  • University of Wisconsin–Madison

Tags

DTIC Thesaurus Topics

  • Banach Space
  • Hilbert Space
  • Mathematics
  • Sequences
  • Stationary

Readers

  • Graph Algorithms and Convex Optimization.
  • Operations Research

Technology Areas

  • Space
  • Space - Space Objects