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

Dan Butnariu; Abraham Mehrez

doi:10.1007/BF00249640

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

Dan Butnariu, Abraham Mehrez

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We prove the convergence of a class of iterative algorithms for solving locally Lipschitz feasibility problems, that is, finite systems of inequalities f_i(x)≤0, (i ∈ I), where each f_i 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 language	English
Pages (from-to)	307-326
Number of pages	20
Journal	Computational Optimization and Applications
Volume	1
Issue number	3
DOIs	https://doi.org/10.1007/BF00249640
State	Published - 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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10.1007/BF00249640

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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]).",

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

author = "Dan Butnariu and Abraham Mehrez",

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AU - Butnariu, Dan

AU - Mehrez, Abraham

PY - 1992/12

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N2 - 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]).

AB - 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]).

KW - (Clarke) generalized derivative

KW - (Clarke) generalized gradient

KW - Locally Lipschitz feasibility problem

KW - convex feasibility problem

KW - generalized gradient method

KW - regularity point, projection method

KW - subgradient method

UR - https://www.scopus.com/pages/publications/0026992276

U2 - 10.1007/BF00249640

DO - 10.1007/BF00249640

M3 - Article

AN - SCOPUS:0026992276

SN - 0926-6003

VL - 1

SP - 307

EP - 326

JO - Computational Optimization and Applications

JF - Computational Optimization and Applications

IS - 3

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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