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Applications of a Splitting Algorithm to Decomposition in Convex Programming and Variational Inequalities
Open accessAbstract
Recently Han and Lou proposed a highly parallelizable decomposition algorithm for minimizing a strongly convex cost over the intersection of closed convex sets. It is shown that their algorithm is in fact a special case of a splitting algorithm analyzed by Gabay for finding a zero of the sum of two maximal monotone operators. Gabay’s convergence analysis for the splitting algorithm is sharpened, and new applications of this algorithm to variational inequalities, convex programming, and the solution of linear complementarily problems are proposed. For convex programs with a certain separable structure, a multiplier method that is closely related to the alternating direction method of multipliers of Gabay–Mercier and of Glowinski–Marrocco, but which uses both ordinary and augmented Lagrangians, is obtained.
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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
Boyd, 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
Alternating Direction Algorithms for $\ell_1$-Problems in Compressive Sensing
Yang, J., & Zhang, Y. (2011) · SIAM Journal on Scientific Computing · doi:10.1137/090777761 · Cited by 1,201
Condat, L. (2013) · Journal of Optimization Theory and Applications · doi:10.1007/s10957-012-0245-9 · Cited by 912
Metadata
- Authors
- Tseng, P.
- Venue
- SIAM Journal on Control and Optimization
- Published
- 1991-01
- Volume
- 29
- Issue
- 1
- Pages
- 119-138
- ISSN
- 0363-0129 (ISSN-L)
- 1095-7138
- OpenAlex
- W1970986119
- Cited by
- 467
- References
- 0
- FWCI
- 2.84
- Type
- journal article
- Language
- en
- Open access
- green
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- Tseng, P. (1991). Applications of a Splitting Algorithm to Decomposition in Convex Programming and Variational Inequalities. SIAM Journal on Control and Optimization. https://doi.org/10.1137/0329006
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