Two generalizations of Dykstra's cyclic projections algorithm

被引：18

作者：

Hundal, H ^{[1
]}

Deutsch, F ^{[1
]}

机构：

[1] PENN STATE UNIV, DEPT MATH, UNIVERSITY PK, PA 16802 USA

来源：

MATHEMATICAL PROGRAMMING | 1997年 / 77卷 / 03期

关键词：

Dykstra's algorithm; cyclic projections; successive approximation; convex feasibility; alternating projections; best approximation; Hildreth's algorithm; finite element method;

D O I：

10.1007/BF02614621

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

Dykstra's cyclic projections algorithm allows one to compute best approximations to any point x in a Hilbert space from the intersection C = boolean AND(1)(r) C-i of a finite number of closed convex sets C-i, by reducing it to a sequence of best approximation problems from the individual sets Ci. Here we present two generalizations of this algorithm. First we allow the number of sets Ci to be infinite rather than finite; secondly, we allow a random, rather than cyclic, ordering of the sets C-1. (C) 1997 The Mathematical Programming Society, Inc.

引用

页码：335 / 355

页数：21

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