Convergence criteria for generalized gradient methods of solving locally Lipschitz feasibility problems

Dan Butnariu, Abraham Mehrez

Research output: Contribution to journalArticlepeer-review

Abstract

We prove the convergence of a class of iterative algorithms for solving locally Lipschitz feasibility problems, that is, finite systems of inequalities fi(x)≤0, (i ∈ I), where each fi is a locally Lipschitz functional on ℝn. We also obtain a new convergence criterion for the so-called block-iterative projection methods of finding common points of finite families of convex closed subsets of ℝn as defined by Aharoni and Censor ([3]).

Original languageEnglish
Pages (from-to)307-326
Number of pages20
JournalComputational Optimization and Applications
Volume1
Issue number3
DOIs
StatePublished - Dec 1992

Keywords

  • (Clarke) generalized derivative
  • (Clarke) generalized gradient
  • Locally Lipschitz feasibility problem
  • convex feasibility problem
  • generalized gradient method
  • regularity point, projection method
  • subgradient method

ASJC Scopus subject areas

  • Control and Optimization
  • Computational Mathematics
  • Applied Mathematics

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