The Dykstra algorithm with Bregman projections

Yair Censor; Simeon Reich

The Dykstra algorithm with Bregman projections

Yair Censor
, Simeon Reich

Department of Mathematics

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

Abstract

Let {Ci| 1≤i≤m} be a finite family of closed convex subsets of Rn, and assume that their intersection C=⋂{Ci| 1≤i≤m} is not empty. In this paper we propose a general Dykstra-type sequential algorithm for finding the Bregman projection of a given point r∈Rn onto C and show that it converges in several important special cases.

Original language	English
Pages (from-to)	407-420
Number of pages	14
Journal	Communications in Applied Analysis
Volume	2
Issue number	3
State	Published - 1998

Cite this

@article{39c794890f86448388440c6cc1faf204,

title = "The Dykstra algorithm with Bregman projections",

abstract = "Let \{Ci| 1≤i≤m\} be a finite family of closed convex subsets of Rn, and assume that their intersection C=⋂\{Ci| 1≤i≤m\} is not empty. In this paper we propose a general Dykstra-type sequential algorithm for finding the Bregman projection of a given point r∈Rn onto C and show that it converges in several important special cases.",

author = "Yair Censor and Simeon Reich",

year = "1998",

language = "English",

volume = "2",

pages = "407--420",

journal = "Communications in Applied Analysis",

issn = "1083-2564",

publisher = "Dynamic Publishers",

number = "3",

}

TY - JOUR

T1 - The Dykstra algorithm with Bregman projections

AU - Censor, Yair

AU - Reich, Simeon

PY - 1998

Y1 - 1998

N2 - Let {Ci| 1≤i≤m} be a finite family of closed convex subsets of Rn, and assume that their intersection C=⋂{Ci| 1≤i≤m} is not empty. In this paper we propose a general Dykstra-type sequential algorithm for finding the Bregman projection of a given point r∈Rn onto C and show that it converges in several important special cases.

AB - Let {Ci| 1≤i≤m} be a finite family of closed convex subsets of Rn, and assume that their intersection C=⋂{Ci| 1≤i≤m} is not empty. In this paper we propose a general Dykstra-type sequential algorithm for finding the Bregman projection of a given point r∈Rn onto C and show that it converges in several important special cases.

UR - http://math.haifa.ac.il/yair/dykstrabreg98.pdf

M3 - Article

SN - 1083-2564

VL - 2

SP - 407

EP - 420

JO - Communications in Applied Analysis

JF - Communications in Applied Analysis

IS - 3

ER -

The Dykstra algorithm with Bregman projections

Abstract

Other files and links

Fingerprint

Cite this