Proximal minimization algorithm with D-functions

Y. Censor; S. A. Zenios

doi:10.1007/BF00940051

Proximal minimization algorithm with D-functions

Y. Censor, S. A. Zenios

Department of Mathematics

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

Abstract

The original proximal minimization algorithm employs quadratic additive terms in the objectives of the subproblems. In this paper, we replace these quadratic additive terms by more general D-functions which resemble (but are not strictly) distance functions. We characterize the properties of such D-functions which, when used in the proximal minimization algorithm, preserve its overall convergence. The quadratic case as well as an entropy-oriented proximal minimization algorithm are obtained as special cases.

Original language	English
Pages (from-to)	451-464
Number of pages	14
Journal	Journal of Optimization Theory and Applications
Volume	73
Issue number	3
DOIs	https://doi.org/10.1007/BF00940051
State	Published - Jun 1992

Keywords

Bregman functions
D-functions
Proximal minimization algorithms
entropy optimization

ASJC Scopus subject areas

Management Science and Operations Research
Control and Optimization
Applied Mathematics

Access to Document

10.1007/BF00940051

Cite this

@article{18fe44f5847e40b08e811c46b3685e96,

title = "Proximal minimization algorithm with D-functions",

abstract = "The original proximal minimization algorithm employs quadratic additive terms in the objectives of the subproblems. In this paper, we replace these quadratic additive terms by more general D-functions which resemble (but are not strictly) distance functions. We characterize the properties of such D-functions which, when used in the proximal minimization algorithm, preserve its overall convergence. The quadratic case as well as an entropy-oriented proximal minimization algorithm are obtained as special cases.",

keywords = "Bregman functions, D-functions, Proximal minimization algorithms, entropy optimization",

author = "Y. Censor and Zenios, {S. A.}",

year = "1992",

month = jun,

doi = "10.1007/BF00940051",

language = "English",

volume = "73",

pages = "451--464",

journal = "Journal of Optimization Theory and Applications",

issn = "0022-3239",

publisher = "Springer New York",

number = "3",

}

TY - JOUR

T1 - Proximal minimization algorithm with D-functions

AU - Censor, Y.

AU - Zenios, S. A.

PY - 1992/6

Y1 - 1992/6

N2 - The original proximal minimization algorithm employs quadratic additive terms in the objectives of the subproblems. In this paper, we replace these quadratic additive terms by more general D-functions which resemble (but are not strictly) distance functions. We characterize the properties of such D-functions which, when used in the proximal minimization algorithm, preserve its overall convergence. The quadratic case as well as an entropy-oriented proximal minimization algorithm are obtained as special cases.

AB - The original proximal minimization algorithm employs quadratic additive terms in the objectives of the subproblems. In this paper, we replace these quadratic additive terms by more general D-functions which resemble (but are not strictly) distance functions. We characterize the properties of such D-functions which, when used in the proximal minimization algorithm, preserve its overall convergence. The quadratic case as well as an entropy-oriented proximal minimization algorithm are obtained as special cases.

KW - Bregman functions

KW - D-functions

KW - Proximal minimization algorithms

KW - entropy optimization

UR - http://www.scopus.com/inward/record.url?scp=0026883817&partnerID=8YFLogxK

U2 - 10.1007/BF00940051

DO - 10.1007/BF00940051

M3 - Article

AN - SCOPUS:0026883817

SN - 0022-3239

VL - 73

SP - 451

EP - 464

JO - Journal of Optimization Theory and Applications

JF - Journal of Optimization Theory and Applications

IS - 3

ER -

Proximal minimization algorithm with D-functions

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this