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Volumn 23, Issue 4, 2013, Pages 2420-2447

Systems of structured monotone inclusions: Duality, algorithms, and applications

Author keywords

Convex minimization; Coupled system; Infimal convolution; Monotone inclusion; Monotone operator; Operator splitting; Parallel algorithm; Structured minimization problem

Indexed keywords

CONVEX MINIMIZATION; COUPLED SYSTEMS; INFIMAL CONVOLUTION; MINIMIZATION PROBLEMS; MONOTONE INCLUSIONS; MONOTONE OPERATORS; OPERATOR-SPLITTING;

EID: 84892839386     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/130904160     Document Type: Article
Times cited : (69)

References (47)
  • 1
    • 10044229927 scopus 로고
    • Convergence d'un schéma de minimisation alternée
    • F. Acker and M. A. Prestel, Convergence d'un schéma de minimisation alternée, Ann. Fac. Sci. Toulouse Math., 2 (1980), pp. 1-9.
    • (1980) Ann. Fac. Sci. Toulouse Math. , vol.2 , pp. 1-9
    • Acker, F.1    Prestel, M.A.2
  • 2
    • 48549093619 scopus 로고    scopus 로고
    • Alternating proximal algorithms for weakly coupled convex minimization problems. Applications to dynamical games and PDE's
    • H. Attouch, J. Bolte, P. Redont, and A. Soubeyran, Alternating proximal algorithms for weakly coupled convex minimization problems. Applications to dynamical games and PDE's, J. Convex Anal., 15 (2008), pp. 485-506.
    • (2008) J. Convex Anal. , vol.15 , pp. 485-506
    • Attouch, H.1    Bolte, J.2    Redont, P.3    Soubeyran, A.4
  • 4
    • 80052802443 scopus 로고    scopus 로고
    • Alternating proximal algorithms for linearly constrained variational inequalities: Application to domain decomposition for PDE's
    • H. Attouch, A. Cabot, P. Frankel, and J. Peypouquet, Alternating proximal algorithms for linearly constrained variational inequalities: Application to domain decomposition for PDE's, Nonlinear Anal., 74 (2011), pp. 7455-7473.
    • (2011) Nonlinear Anal. , vol.74 , pp. 7455-7473
    • Attouch, H.1    Cabot, A.2    Frankel, P.3    Peypouquet, J.4
  • 5
    • 48549105307 scopus 로고    scopus 로고
    • A new class of alternating proximal minimization algorithms with costs-to-move
    • H. Attouch, P. Redont, and A. Soubeyran, A new class of alternating proximal minimization algorithms with costs-to-move, SIAM J. Optim., 18 (2007), pp. 1061-1081.
    • (2007) SIAM J. Optim. , vol.18 , pp. 1061-1081
    • Attouch, H.1    Redont, P.2    Soubeyran, A.3
  • 7
    • 0000651929 scopus 로고
    • The solution of variational inequalities
    • A. B. Bakušinskiǐ and B. T. Polyak, The solution of variational inequalities, Soviet Math. -Doklady, 15 (1974), pp. 1705-1710.
    • (1974) Soviet Math. -Doklady , vol.15 , pp. 1705-1710
    • Bakušinskiǐ, A.B.1    Polyak, B.T.2
  • 9
    • 2942687455 scopus 로고    scopus 로고
    • Finding best approximation pairs relative to two closed convex sets in Hilbert spaces
    • H. H. Bauschke, P. L. Combettes, and D. R. Luke, Finding best approximation pairs relative to two closed convex sets in Hilbert spaces, J. Approx. Theory, 127 (2004), pp. 178-192.
    • (2004) J. Approx. Theory , vol.127 , pp. 178-192
    • Bauschke, H.H.1    Combettes, P.L.2    Luke, D.R.3
  • 10
    • 10044229235 scopus 로고    scopus 로고
    • The asymptotic behavior of the composition of two resolvents
    • H. H. Bauschke, P. L. Combettes, and S. Reich, The asymptotic behavior of the composition of two resolvents, Nonlinear Anal., 60 (2005), pp. 283-301.
    • (2005) Nonlinear Anal. , vol.60 , pp. 283-301
    • Bauschke, H.H.1    Combettes, P.L.2    Reich, S.3
  • 11
    • 84892898174 scopus 로고    scopus 로고
    • An algorithm for splitting parallel sums of linearly composed monotone operators, with applications to signal recovery
    • to appear
    • S. R. Becker and P. L. Combettes, An algorithm for splitting parallel sums of linearly composed monotone operators, with applications to signal recovery, J. Convex Nonlinear Anal., to appear.
    • J. Convex Nonlinear Anal.
    • Becker, S.R.1    Combettes, P.L.2
  • 12
    • 0012178656 scopus 로고
    • Méthodes d'approximation et d'itération pour les opérateurs monotones
    • H. Brézis and M. Sibony, Méthodes d'approximation et d'itération pour les opérateurs monotones, Arch. Ration. Mech. Anal., 28 (1967/1968), pp. 59-82.
    • (1967) Arch. Ration. Mech. Anal. , vol.28 , pp. 59-82
    • Brézis, H.1    Sibony, M.2
  • 13
    • 78651107831 scopus 로고    scopus 로고
    • Convex variational formulation with smooth coupling for multicomponent signal decomposition and recovery
    • L. M. Briceño-Arias and P. L. Combettes, Convex variational formulation with smooth coupling for multicomponent signal decomposition and recovery, Numer. Math. Theory Methods Appl., 2 (2009), pp. 485-508.
    • (2009) Numer. Math. Theory Methods Appl. , vol.2 , pp. 485-508
    • Briceño-Arias, L.M.1    Combettes, P.L.2
  • 14
    • 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
  • 16
    • 84864229832 scopus 로고    scopus 로고
    • Image restoration: Total variation, wavelet frames, and beyond
    • J.-F. Cai, B. Dong, S. Osher, and Z. Shen, Image restoration: Total variation, wavelet frames, and beyond, J. Amer. Math. Soc., 25 (2012), pp. 1033-1089.
    • (2012) J. Amer. Math. Soc. , vol.25 , pp. 1033-1089
    • Cai, J.-F.1    Dong, B.2    Osher, S.3    Shen, Z.4
  • 17
    • 0001488677 scopus 로고
    • Construction d'un point fixe commun à une famille de contractions fermes
    • P. L. Combettes, Construction d'un point fixe commun à une famille de contractions fermes, C. R. Acad. Sci. Paris Sér. I Math., 320 (1995), pp. 1385-1390.
    • (1995) C. R. Acad. Sci. Paris Sér. i Math. , vol.320 , pp. 1385-1390
    • Combettes, P.L.1
  • 18
    • 13244295576 scopus 로고    scopus 로고
    • Solving monotone inclusions via compositions of nonexpansive averaged operators
    • P. L. Combettes, Solving monotone inclusions via compositions of nonexpansive averaged operators, Optimization, 53 (2004), pp. 475-504.
    • (2004) Optimization , vol.53 , pp. 475-504
    • Combettes, P.L.1
  • 19
    • 0032653272 scopus 로고    scopus 로고
    • Hard-constrained inconsistent signal feasibility problems
    • P. L. Combettes and P. Bondon, Hard-constrained inconsistent signal feasibility problems, IEEE Trans. Signal Process., 47 (1999), pp. 2460-2468.
    • (1999) IEEE Trans. Signal Process. , vol.47 , pp. 2460-2468
    • Combettes, P.L.1    Bondon, P.2
  • 20
    • 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
  • 21
    • 30844438177 scopus 로고    scopus 로고
    • Signal recovery by proximal forward-backward splitting
    • P. L. Combettes and V. R. Wajs, Signal recovery by proximal forward-backward splitting, Multiscale Model. Simul., 4 (2005), pp. 1168-1200.
    • (2005) Multiscale Model. Simul. , vol.4 , pp. 1168-1200
    • Combettes, P.L.1    Wajs, V.R.2
  • 22
    • 84967782959 scopus 로고
    • On the numerical solution of heat conduction problems in two or three space variables
    • J. Douglas, Jr., and H. H. Rachford, Jr., On the numerical solution of heat conduction problems in two or three space variables, Trans. Amer. Math. Soc., 82 (1956), pp. 421-439.
    • (1956) Trans. Amer. Math. Soc. , vol.82 , pp. 421-439
    • Douglas Jr., J.1    Rachford Jr., H.H.2
  • 23
    • 0040663105 scopus 로고
    • Unrestricted iterations of nonexpansive mappings in Hilbert space
    • J. M. Dye and S. Reich, Unrestricted iterations of nonexpansive mappings in Hilbert space, Nonlinear Anal., 18 (1992), pp. 199-207.
    • (1992) Nonlinear Anal. , vol.18 , pp. 199-207
    • Dye, J.M.1    Reich, S.2
  • 24
    • 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
  • 26
    • 84864474528 scopus 로고    scopus 로고
    • Alternating proximal algorithm with costs-to-move, dual description and application to PDE's
    • P. Frankel, Alternating proximal algorithm with costs-to-move, dual description and application to PDE's, Discrete Contin. Dyn. Syst. Ser. S, 5 (2012), pp. 545-557.
    • (2012) Discrete Contin. Dyn. Syst. Ser. S , vol.5 , pp. 545-557
    • Frankel, P.1
  • 28
    • 35548973888 scopus 로고    scopus 로고
    • Noisy image decomposition: A new structure, texture and noise model based on local adaptivity
    • J. Gilles, Noisy image decomposition: A new structure, texture and noise model based on local adaptivity, J. Math. Imaging Vision, 28 (2007), pp. 285-295.
    • (2007) J. Math. Imaging Vision , vol.28 , pp. 285-295
    • Gilles, J.1
  • 30
    • 0022091196 scopus 로고
    • Signal synthesis in the presence of an inconsistent set of constraints
    • M. Goldburg and R. J. Marks II, Signal synthesis in the presence of an inconsistent set of constraints, IEEE Trans. Circuits Systems, 32 (1985), pp. 647-663.
    • (1985) IEEE Trans. Circuits Systems , vol.32 , pp. 647-663
    • Goldburg, M.1    Marks II, R.J.2
  • 31
    • 0000005602 scopus 로고
    • The extragradient method for finding saddle points and other problems
    • G. M. Korpelevich, The extragradient method for finding saddle points and other problems, Matecon, 12 (1976), pp. 747-756.
    • (1976) Matecon , vol.12 , pp. 747-756
    • Korpelevich, G.M.1
  • 35
    • 0000345334 scopus 로고
    • Splitting algorithms for the sum of two nonlinear operators
    • P.-L. Lions and B. Mercier, Splitting algorithms for the sum of two nonlinear operators, SIAM J. Numer. Anal., 16 (1979), pp. 964-979.
    • (1979) SIAM J. Numer. Anal. , vol.16 , pp. 964-979
    • Lions, P.-L.1    Mercier, B.2
  • 36
    • 0039630337 scopus 로고
    • Partial regularization of the sum of two maximal monotone operators
    • P. Mahey and D. T. Pham, Partial regularization of the sum of two maximal monotone operators, RAIRO Modél. Math. Anal. Numér., 27 (1993), pp. 375-392.
    • (1993) RAIRO Modél. Math. Anal. Numér. , vol.27 , pp. 375-392
    • Mahey, P.1    Pham, D.T.2
  • 37
    • 0345934041 scopus 로고
    • Topics in finite element solution of elliptic problems
    • Tata Institute of Fundamental Research, Bombay
    • B. Mercier, Topics in Finite Element Solution of Elliptic Problems, Lectures on Mathematics, 63, Tata Institute of Fundamental Research, Bombay, 1979.
    • (1979) Lectures on Mathematics , pp. 63
    • Mercier, B.1
  • 38
    • 10044295538 scopus 로고
    • Publications Mathématiques d'Orsay 80.01, Université de Paris-XI, Orsay, France
    • B. Mercier, Inéquations Variationnelles de la Mécanique, Publications Mathématiques d'Orsay 80.01, Université de Paris-XI, Orsay, France, 1980.
    • (1980) Inéquations Variationnelles de la Mécanique
    • Mercier, B.1
  • 40
    • 51249189125 scopus 로고
    • Méthodes itératives pour les équations et inéquations aux dérivées partielles non linéaires de type monotone
    • M. Sibony, Méthodes itératives pour les équations et inéquations aux dérivées partielles non linéaires de type monotone, Calcolo, 7 (1970), pp. 65-183.
    • (1970) Calcolo , vol.7 , pp. 65-183
    • Sibony, M.1
  • 41
    • 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
  • 42
    • 27744574209 scopus 로고    scopus 로고
    • Image decomposition via the combination of sparse representations and a variational approach
    • J.-L. Starck, M. Elad, and D. L. Donoho, Image decomposition via the combination of sparse representations and a variational approach, IEEE Trans. Image Process., 14 (2005), pp. 1570-1582.
    • (2005) IEEE Trans. Image Process. , vol.14 , pp. 1570-1582
    • Starck, J.-L.1    Elad, M.2    Donoho, D.L.3
  • 43
    • 0026077016 scopus 로고
    • Applications of a splitting algorithm to decomposition in convex programming and variational inequalities
    • P. Tseng, Applications of a splitting algorithm to decomposition in convex programming and variational inequalities, SIAM J. Control Optim., 29 (1991), pp. 119-138.
    • (1991) SIAM J. Control Optim. , vol.29 , pp. 119-138
    • Tseng, P.1
  • 44
    • 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
  • 46
    • 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


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