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Augmented Lagrangians and Applications of the Proximal Point Algorithm in Convex Programming
Abstract
The theory of the proximal point algorithm for maximal monotone operators is applied to three algorithms for solving convex programs, one of which has not previously been formulated. Rate-of-convergence results for the “method of multipliers,” of the strong sort already known, are derived in a generalized form relevant also to problems beyond the compass of the standard second-order conditions for oplimality. The new algorithm, the “proximal method of multipliers,” is shown to have much the same convergence properties, but with some potential advantages.
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Citations
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
Parikh, N., & Boyd, S. (2014) · Foundations and Trends® in Optimization · doi:10.1561/2400000003 · Cited by 4,102
Conn, A. R., Gould, N. I. M., & Toint, P. (1991) · SIAM Journal on Numerical Analysis · doi:10.1137/0728030 · Cited by 873
Error bounds and convergence analysis of feasible descent methods: a general approach
Luo, Z.-Q., & Tseng, P. (1993) · Annals of Operations Research · doi:10.1007/bf02096261 · Cited by 420
Linear Convergence Rate of a Class of Distributed Augmented Lagrangian Algorithms
Jakovetic, D., Moura, J. M. F., & Xavier, J. (2015) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2014.2363299 · Cited by 123
Metadata
- Authors
- Rockafellar, R. T.
- Venue
- Mathematics of Operations Research
- Published
- 1976-05
- Volume
- 1
- Issue
- 2
- Pages
- 97-116
- ISSN
- 0364-765X (ISSN-L)
- 1526-5471
- OpenAlex
- W2135779729
- Cited by
- 1,175
- References
- 0
- FWCI
- 3.22
- Type
- journal article
- Language
- en
- Open access
- closed
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- CoChat. (2026). Citation check: Augmented Lagrangians and Applications of the Proximal Point Algorithm in Convex Programming. https://app.cochat.ai/papers/10.1287/moor.1.2.97
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- Rockafellar, R. T. (1976). Augmented Lagrangians and Applications of the Proximal Point Algorithm in Convex Programming. Mathematics of Operations Research. https://doi.org/10.1287/moor.1.2.97
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