REMARKS ON THE GRADIENT-PROJECTION ALGORITHM

Authors

  • Meng Su PENNSTATEUNIVERSITY ATERIE, THEBEHRENDCOLLEGE, 4205 COLLEGEDRIVE, ERIE, PA 16563-0203,U.S.A.
  • Hong-Kun Xu DEPARTMENT OFAPPLIEDMATHEMATICS, NATIONALSUNYAT-SENUNIVERSITY, KAOHSIUNG80424, TAI-WAN

Keywords:

Gradient-projection algorithm, constrained minimization, variational inequality, optimality condition, convex function, LipsLichitz continuous gradient, F ́ejer-monotone

Abstract

The gradient-projection algorithm (GPA) is a powerful method for solving constrained minimization problems infinite (and even infinite) dimensional Hilbert spaces. We consider GPA with variable stepsizes and show that if GPA generates a bounded sequence, then under certain assumptions, every accumulation point of the sequence is a solution of the minimization problem. We also look into the issue where the sequence of step sizes is allowed to be the limiting case (e.g., approaching to zero).

Additional Files

Published

12/09/2011

Issue

Vol. 1 No. 1 (2010): JNAO

Section

Research Articles

License

Copyright (c) 2024 Journal of Nonlinear Analysis and Optimization: Theory & Applications (JNAO)

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Copyright (c) 2010 Journal of Nonlinear Analysis and Optimization: Theory & Applications

Creative Commons License

This work is licensed under aย Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.