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In this paper, we establish the convergence properties for a majorized alternating direction method of multipliers (ADMM) for linearly constrained convex optimization problems whose objectives contain coupled functions.
1911
Earlier work this paper cites.
Glowinski, R. and Marroco, A. (1975). Sur l’approximation, par elements finis d’ordre un, et la resolution, par penalisation-dualit’e, d’une classe de problemes de Dirichlet non lineares, Revue Francaise d’Automatique, Informatique et Recherche Op’erationelle. 9 (R-2), pp. 41–76
1975
Earlier work this paper cites.
Gabay, D. and Mercier, B. (1976). A dual algorithm for the solution of nonlinear variational problems via finite element approximation, Computers and Mathematics with Applications, 2(1), 17-40
1976
Earlier work this paper cites.
Notes by M. G. Vijayasundaram and M. Adimurthi
Glowinski, R. (1980). Lectures on numerical methods for nonlinear variational problems, vol. 65 of Tata Institute of Fundamental Research Lectures on Mathematics and Physics, Tata Institute of Fundamental Research, Bombay, · 1980
Earlier work this paper cites.
Gabay, D. (1983). Applications of the method of multipliers to variational inequalities, in Augmented Lagrangian Methods: Applications to the Numerical Solution of Boundary-Value Problems, M. Fortin and R. Glowinski, eds., vol. 15 of Studies in Mathematics and Its Applications, Elsevier, pp. 299-331
1983
Earlier work this paper cites.
Hiriart-Urruty, J. B., Strodiot, J. J. and Nguyen, V. H. (1984). Generalized Hessian matrix and second-order optimality conditions for problems with C 1 , 1 C^{1,1} data, Applied mathematics and optimization, 11(1), 43-56
1984
Earlier work this paper cites.
Clarke, F, H. (1990). Optimization and Nonsmooth Analysis, 2nd edition, Classics in Applied Mathematics, vol. 5, Society for Industrial and Applied Mathematics, Philadelphia
1990
Cited alongside, same era.
Eckstein, J. and Bertsekas, D. P. (1992). On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators. Mathematical Programming, 55(1-3), 293-318
1992
Cited alongside, same era.
He, B. and Yuan, X. (2012). On the O ( 1 / n ) O(1/n) Convergence Rate of the Douglas-Rachford Alternating Direction Method, SIAM Journal on Numerical Analysis, 50(2), 700-709
2012
Cited alongside, same era.
Monteiro, R. D. and Svaiter, B. F. (2013). Iteration-complexity of block-decomposition algorithms and the alternating direction method of multipliers, SIAM Journal on Optimization, 23(1), 475-507
2013
Cited alongside, same era.
Chen, C., He, B., Ye, Y. and Yuan, X. (2014). The direct extension of ADMM for multi-block convex minimization problems is not necessarily convergent, Mathematical Programming, Series A, DOI 10.1007/s10107-014-0826-5
2014
Later among the works it cites.
2014
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Eckstein, J. and Yao, W. (2014). Understanding the convergence of the alternating direction method of multipliers: Theoretical and computational perspectives, RUTCOR Research Report
2014
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2014
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Nesterov, Y. (2013). Gradient methods for minimizing composite functions. Mathematical Programming, Series B, 140(1), 125-161
2013
Cited alongside, same era.
Li, X. D., Sun, D. F. and Toh, K. C. (2014). A Schur Complement Based Semi-Proximal ADMM for Convex Quadratic Conic Programming and Extensions, Mathematical Programming, Series A, DOI 10.1007/s10107-014-0850-5
2014
Later among the works it cites.