The DOI matches its Crossref record; 19 of the 19 references it cites were found in a registry or an index.
Nonlinear Proximal Point Algorithms Using Bregman Functions, with Applications to Convex Programming
Abstract
A Bregman function is a strictly convex, differentiable function that induces a well-behaved distance measure or D-function on Euclidean space. This paper shows that, for every Bregman function, there exists a “nonlinear” version of the proximal point algorithm, and presents an accompanying convergence theory. Applying this generalization of the proximal point algorithm to convex programming, one obtains the D-function proximal minimization algorithm of Censor and Zenios, and a wide variety of new multiplier methods. These multiplier methods are different from those studied by Kort and Bertsekas, and include nonquadratic variations on the proximal method of multipliers.
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Cites
Constrained Optimization and Lagrange Multiplier Methods
(1982) · Elsevier eBooks · doi:10.1016/c2013-0-10366-2 · Cited by 4,016
Monotone Operators and the Proximal Point Algorithm
Rockafellar, R. T. (1976) · SIAM Journal on Control and Optimization · doi:10.1137/0314056 · Cited by 3,559
Eckstein, J., & Bertsekas, D. P. (1992) · Mathematical Programming · doi:10.1007/bf01581204 · Cited by 2,791
Self-citationBregman, L. M. (1967) · USSR Computational Mathematics and Mathematical Physics · doi:10.1016/0041-5553(67)90040-7 · Cited by 2,618
Operateurs Maximaux Monotones - Et Semi-Groupes De Contractions Dans Les Espaces De Hilbert
(1973) · North-Holland Mathematics Studies · doi:10.1016/s0304-0208(08)x7125-7 · Cited by 2,578
Multiplier and gradient methods
Hestenes, M. R. (1969) · Journal of Optimization Theory and Applications · doi:10.1007/bf00927673 · Cited by 2,446
(2002) · Springer eBooks · doi:10.1007/b114992 · Cited by 1,881
Augmented Lagrangians and Applications of the Proximal Point Algorithm in Convex Programming
Rockafellar, R. T. (1976) · Mathematics of Operations Research · doi:10.1287/moor.1.2.97 · Cited by 1,175
On the maximality of sums of nonlinear monotone operators
Rockafellar, R. T. (1970) · Transactions of the American Mathematical Society · doi:10.1090/s0002-9947-1970-0282272-5 · Cited by 949
On the maximal monotonicity of subdifferential mappings
Rockafellar, R. (1970) · Pacific Journal of Mathematics · doi:10.2140/pjm.1970.33.209 · Cited by 740
Cited by
Boyd, S., Parikh, N., Chu, E., Peleato, B., & Eckstein, J. (2011) · Foundations and Trends® in Machine Learning · doi:10.1561/2200000016 · Cited by 17,075
Self-citationBoyd, S. (2010) · now publishers, Inc. eBooks · doi:10.1561/9781601984616 · Cited by 12,677
Parikh, N., & Boyd, S. (2014) · Foundations and Trends® in Optimization · doi:10.1561/2400000003 · Cited by 4,102
Convergence Analysis of a Proximal-Like Minimization Algorithm Using Bregman Functions
Chen, G., & Teboulle, M. (1993) · SIAM Journal on Optimization · doi:10.1137/0803026 · Cited by 428
On the ergodic convergence rates of a first-order primal–dual algorithm
Chambolle, A., & Pock, T. (2016) · Mathematical Programming · doi:10.1007/s10107-015-0957-3 · Cited by 411
Metadata
- Authors
- Eckstein, J.
- Venue
- Mathematics of Operations Research
- Published
- 1993-02
- Volume
- 18
- Issue
- 1
- Pages
- 202-226
- ISSN
- 0364-765X (ISSN-L)
- 1526-5471
- OpenAlex
- W2112980792
- Cited by
- 324
- References
- 19
- FWCI
- 9.03
- Type
- journal article
- Language
- en
- Open access
- closed
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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