Successive Projection under a Quasi-Cyclic Order

Abstract

A classical method for finding a point in the intersection of a finite collection of closed convex sets is the successive projection method. It is well-known that this method is convergent if each convex sets is chosen for projection in a cyclical manner. In this note we show that this method is still convergent if the length of the cycle grows without bound, provided that the growth is not too fast. Our argument is based on an interesting application of the Cauchy-Schwartz inequality.

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Document Details

Document Type
Technical Report
Publication Date
Jan 06, 1990
Accession Number
ADA458804

Entities

People

  • Paul Tseng

Organizations

  • Massachusetts Institute of Technology

Tags

Communities of Interest

  • Autonomy

DTIC Thesaurus Topics

  • Algorithms
  • Convergence
  • Convex Programming
  • Convex Sets
  • Geometry
  • Hilbert Space
  • Image Reconstruction
  • Inequalities
  • Information Operations
  • Iterations
  • Machine Learning
  • New York
  • Quadratic Programming
  • Sequences
  • Theorems
  • Topology
  • Weak Convergence

Fields of Study

  • Mathematics

Readers

  • Graph Algorithms and Convex Optimization.
  • Theoretical Analysis.