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Volumn 23, Issue 4, 2013, Pages 2011-2036

A primal-dual splitting algorithm for finding zeros of sums of maximal monotone operators

Author keywords

Duality; Maximal monotone operator; Minimization algorithm; Operator splitting; Resolvent; Subdifferential

Indexed keywords

DUALITY; MAXIMAL MONOTONE OPERATORS; MINIMIZATION ALGORITHMS; OPERATOR-SPLITTING; RESOLVENT; SUBDIFFERENTIALS;

EID: 84891044364     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/12088255X     Document Type: Article
Times cited : (77)

References (31)
  • 1
    • 23244441408 scopus 로고    scopus 로고
    • Composition duality principles for mixed variational inequalities
    • G. Alduncin, Composition duality principles for mixed variational inequalities, Math. Comput. Modelling, 41 (2005), pp. 639-654.
    • (2005) Math. Comput. Modelling , vol.41 , pp. 639-654
    • Alduncin, G.1
  • 2
    • 0039041998 scopus 로고
    • Studies in linear and nonlinear programming
    • Stanford University Press, Stanford, CA
    • K. J. Arrow, L. Hurwicz, and H. Uzawa, Studies in Linear and Nonlinear Programming, Stanford Math. Stud. Social Sci., Stanford University Press, Stanford, CA, 1958.
    • (1958) Stanford Math. Stud. Social Sci.
    • Arrow, K.J.1    Hurwicz, L.2    Uzawa, H.3
  • 3
    • 0347211614 scopus 로고    scopus 로고
    • A general duality principle for the sum of two operators
    • H. Attouch and M. Théra, A general duality principle for the sum of two operators, J. Convex Anal., 3 (1996), pp. 1-24.
    • (1996) J. Convex Anal. , vol.3 , pp. 1-24
    • Attouch, H.1    Théra, M.2
  • 4
    • 84862884952 scopus 로고    scopus 로고
    • Attouch-Théra duality revisited: Paramonotonicity and operator splitting
    • H. H. Bauschke, R. I. Boţ, W. L. Hare, and W. M. Moursi, Attouch-Théra duality revisited: Paramonotonicity and operator splitting, J. Approx. Theory, 164 (2012), pp. 1065-1084.
    • (2012) J. Approx. Theory , vol.164 , pp. 1065-1084
    • Bauschke, H.H.1    Boţ, R.I.2    Hare, W.L.3    Moursi, W.M.4
  • 6
    • 77949571044 scopus 로고    scopus 로고
    • Conjugate duality in convex optimization
    • Springer, Berlin, Heidelberg
    • R. I. Boţ, Conjugate Duality in Convex Optimization, Lecture Notes in Econom. and Math. Systems 637, Springer, Berlin, Heidelberg, 2010.
    • (2010) Lecture Notes in Econom. and Math. Systems , vol.637
    • Boţ, R.I.1
  • 7
    • 84856817068 scopus 로고    scopus 로고
    • Regularity conditions via generalized interiority notions in convex optimization: New achievements and their relation to some classical statements
    • R. I. Boţ and E. R. Csetnek, Regularity conditions via generalized interiority notions in convex optimization: New achievements and their relation to some classical statements, Optimization, 61 (2012), pp. 35-65.
    • (2012) Optimization , vol.61 , pp. 35-65
    • Boţ, R.I.1    Csetnek, E.R.2
  • 9
    • 80051762104 scopus 로고    scopus 로고
    • Distributed optimization and statistical learning via the alternating direction method of multipliers
    • S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein, Distributed optimization and statistical learning via the alternating direction method of multipliers, Found. Trends Mach. Learning, 3 (2010), pp. 1-122.
    • (2010) Found. Trends Mach. Learning , vol.3 , pp. 1-122
    • Boyd, S.1    Parikh, N.2    Chu, E.3    Peleato, B.4    Eckstein, J.5
  • 10
    • 84855933316 scopus 로고    scopus 로고
    • A monotone + skew splitting model for composite monotone inclusions in duality
    • L. M. Briceño-Arias and P. L. Combettes, A monotone + skew splitting model for composite monotone inclusions in duality, SIAM J. Optim., 21 (2011), pp. 1230-1250.
    • (2011) SIAM J. Optim. , vol.21 , pp. 1230-1250
    • Briceño-Arias, L.M.1    Combettes, P.L.2
  • 11
    • 1242352408 scopus 로고    scopus 로고
    • An algorithm for total variation minimization and applications
    • A. Chambolle, An algorithm for total variation minimization and applications, J. Math. Imaging Vision, 20 (2004), pp. 89-97.
    • (2004) J. Math. Imaging Vision , vol.20 , pp. 89-97
    • Chambolle, A.1
  • 12
    • 79953201848 scopus 로고    scopus 로고
    • A first-order primal-dual algorithm for convex problems with applications to imaging
    • A. Chambolle and T. Pock, A first-order primal-dual algorithm for convex problems with applications to imaging, J. Math. Imaging Vision, 40 (2011), pp. 120-145.
    • (2011) J. Math. Imaging Vision , vol.40 , pp. 120-145
    • Chambolle, A.1    Pock, T.2
  • 13
    • 84869774172 scopus 로고    scopus 로고
    • Primal-dual splitting algorithm for solving inclusions with mixtures of composite, Lipschitzian, and parallel-sum type monotone operators
    • P. L. Combettes and J.-C. Pesquet, Primal-dual splitting algorithm for solving inclusions with mixtures of composite, Lipschitzian, and parallel-sum type monotone operators, Set-Valued Var. Anal., 20 (2012), pp. 307-330.
    • (2012) Set-Valued Var. Anal. , vol.20 , pp. 307-330
    • Combettes, P.L.1    Pesquet, J.-C.2
  • 14
    • 84967782959 scopus 로고
    • On the numerical solution of the heat conduction problem in 2 and 3 space variables
    • J. Douglas and H. H. Rachford, On the numerical solution of the heat conduction problem in 2 and 3 space variables, Trans. Amer. Math. Soc., 82 (1956), pp. 421-439.
    • (1956) Trans. Amer. Math. Soc. , vol.82 , pp. 421-439
    • Douglas, J.1    Rachford, H.H.2
  • 15
    • 0029548475 scopus 로고
    • A note on accelerating the Weiszfeld procedure
    • Z. Drezner, A note on accelerating the Weiszfeld procedure, Location Sci., 3 (1995), pp. 275-279.
    • (1995) Location Sci. , vol.3 , pp. 275-279
    • Drezner, Z.1
  • 16
    • 84892888999 scopus 로고    scopus 로고
    • Augmented lagrangian and alternating direction methods for convex optimization: A tutorial and some illustrative computational results
    • Rutgers University
    • J. Eckstein, Augmented Lagrangian and Alternating Direction Methods for Convex Optimization: A Tutorial and Some Illustrative Computational Results, Rutcor Research Report 32-2012, Rutgers University, 2012.
    • (2012) Rutcor Research Report 32-2012
    • Eckstein, J.1
  • 17
    • 0027113845 scopus 로고
    • On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators
    • J. Eckstein and D. P. Bertsekas, On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators, Math. Program., 55 (1992), pp. 293-318.
    • (1992) Math. Program. , vol.55 , pp. 293-318
    • Eckstein, J.1    Bertsekas, D.P.2
  • 18
    • 0001871553 scopus 로고    scopus 로고
    • Smooth methods of multipliers for complementarity problems
    • J. Eckstein and M. C. Ferris, Smooth methods of multipliers for complementarity problems, Math. Program., 86 (1999), pp. 65-90.
    • (1999) Math. Program. , vol.86 , pp. 65-90
    • Eckstein, J.1    Ferris, M.C.2
  • 20
    • 80051766714 scopus 로고    scopus 로고
    • A general framework for a class of first order primaldual algorithms for convex optimization in imaging science
    • E. Esser, X. Zhang, and T. F. Chan, A general framework for a class of first order primaldual algorithms for convex optimization in imaging science, SIAM J. Imaging Sci., 3 (2010), pp. 1015-1046.
    • (2010) SIAM J. Imaging Sci. , vol.3 , pp. 1015-1046
    • Esser, E.1    Zhang, X.2    Chan, T.F.3
  • 21
    • 84865692740 scopus 로고    scopus 로고
    • Fast multiple-splitting algorithms for convex optimization
    • D. Goldfarb and S. Ma, Fast multiple-splitting algorithms for convex optimization, SIAM J. Optim., 22 (2012), pp. 533-556.
    • (2012) SIAM J. Optim. , vol.22 , pp. 533-556
    • Goldfarb, D.1    Ma, S.2
  • 24
    • 0034403146 scopus 로고    scopus 로고
    • Dualization of generalized equations of maximal monotone type
    • T. Pennanen, Dualization of generalized equations of maximal monotone type, SIAM J. Optim., 10 (2000), pp. 809-835.
    • (2000) SIAM J. Optim. , vol.10 , pp. 809-835
    • Pennanen, T.1
  • 25
    • 84972582929 scopus 로고
    • On the maximal monotonicity of subdifferential mappings
    • R. T. Rockafellar, On the maximal monotonicity of subdifferential mappings, Pacific J. Math., 33 (1970), pp. 209-216.
    • (1970) Pacific J. Math. , vol.33 , pp. 209-216
    • Rockafellar, R.T.1
  • 27
    • 0001531775 scopus 로고
    • Partial inverse of a monotone operator
    • J. E. Spingarn, Partial inverse of a monotone operator, Appl. Math. Optim., 10 (1983), pp. 247-265.
    • (1983) Appl. Math. Optim. , vol.10 , pp. 247-265
    • Spingarn, J.E.1
  • 28
    • 0033884548 scopus 로고    scopus 로고
    • A modified forward-backward splitting method for maximal monotone mappings
    • P. Tseng, A modified forward-backward splitting method for maximal monotone mappings, SIAM J. Control Optim., 38 (2000), pp. 431-446.
    • (2000) SIAM J. Control Optim. , vol.38 , pp. 431-446
    • Tseng, P.1
  • 29
    • 84875493148 scopus 로고    scopus 로고
    • A splitting algorithm for dual monotone inclusions involving cocoercive operators
    • B. C. Vũ, A splitting algorithm for dual monotone inclusions involving cocoercive operators, Adv. Comput. Math., 38 (2013), pp. 667-681.
    • (2013) Adv. Comput. Math. , vol.38 , pp. 667-681
    • Vũ, B.C.1
  • 30
    • 0000281286 scopus 로고
    • Sur le point pour lequel la somme des distances de n points donnes est minimum
    • E. Weiszfeld, Sur le point pour lequel la somme des distances de n points donnes est minimum, Tohoku Math. J., 43 (1937), pp. 597-609.
    • (1937) Tohoku Math. J. , vol.43 , pp. 597-609
    • Weiszfeld, E.1


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