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Volumn 64, Issue 5, 2015, Pages 1239-1261

Forward-Douglas–Rachford splitting and forward-partial inverse method for solving monotone inclusions

Author keywords

composite operator; convex optimization; minimization algorithm; monotone inclusion; partial inverse; splitting methods

Indexed keywords


EID: 84924242240     PISSN: 02331934     EISSN: 10294945     Source Type: Journal    
DOI: 10.1080/02331934.2013.855210     Document Type: Article
Times cited : (85)

References (48)
  • 1
    • 62649171652 scopus 로고    scopus 로고
    • A proximal decomposition method for solving convex variational inverse problems
    • 27p
    • Combettes PL, Pesquet J-C. A proximal decomposition method for solving convex variational inverse problems. Inverse Prob. 2008;24:065014, 27p.
    • (2008) Inverse Prob , vol.24 , pp. 065014
    • Combettes, P.L.1    Pesquet, J.-C.2
  • 2
    • 0022076946 scopus 로고
    • Applications of the method of partial inverses to convex programming: decomposition
    • Spingarn JE. Applications of the method of partial inverses to convex programming: decomposition. Math. Program. 1985;32:199–223.
    • (1985) Math. Program , vol.32 , pp. 199-223
    • Spingarn, J.E.1
  • 4
    • 0000626995 scopus 로고
    • Further applications of a splitting algorithm to decomposition in variational inequalities and convex programming
    • Tseng P. Further applications of a splitting algorithm to decomposition in variational inequalities and convex programming. Math. Program. 1990;48:249–263.
    • (1990) Math. Program , vol.48 , pp. 249-263
    • Tseng, P.1
  • 5
    • 0026077016 scopus 로고
    • Applications of a splitting algorithm to decomposition in convex programming and variational inequalities
    • Tseng P. Applications of a splitting algorithm to decomposition in convex programming and variational inequalities. SIAM J. Control Optim. 1991;29:119–138.
    • (1991) SIAM J. Control Optim , vol.29 , pp. 119-138
    • Tseng, P.1
  • 6
    • 34249837486 scopus 로고
    • On the Douglas–Rachford splitting method and the proximal point algorithm for maximal monotone operators
    • Eckstein J, Bertsekas DP. On the Douglas–Rachford splitting method and the proximal point algorithm for maximal monotone operators. Math. Program. 1992;55:293–318.
    • (1992) Math. Program , vol.55 , pp. 293-318
    • Eckstein, J.1    Bertsekas, D.P.2
  • 7
    • 0000345334 scopus 로고
    • Splitting algorithms for the sum of two nonlinear operators
    • Lions P-L, Mercier B. Splitting algorithms for the sum of two nonlinear operators. SIAM J. Numer. Anal. 1979;16:964–979.
    • (1979) SIAM J. Numer. Anal , vol.16 , pp. 964-979
    • Lions, P.-L.1    Mercier, B.2
  • 8
    • 0016985417 scopus 로고
    • Monotone operators and the proximal point algorithm
    • Rockafellar RT. Monotone operators and the proximal point algorithm. SIAM J. Control Optim. 1976;14:877–898.
    • (1976) SIAM J. Control Optim , vol.14 , pp. 877-898
    • Rockafellar, R.T.1
  • 9
    • 0001531775 scopus 로고
    • Partial inverse of a monotone operator
    • Spingarn JE. Partial inverse of a monotone operator. Appl. Math. Optim. 1983;10:247–265.
    • (1983) Appl. Math. Optim , vol.10 , pp. 247-265
    • Spingarn, J.E.1
  • 15
    • 84865699264 scopus 로고    scopus 로고
    • Introduction to convex optimization in financial markets
    • Pennanen T. Introduction to convex optimization in financial markets. Math. Program. 2012;134:157–186.
    • (2012) Math. Program , vol.134 , pp. 157-186
    • Pennanen, T.1
  • 16
    • 33644533840 scopus 로고    scopus 로고
    • Structure-texture image decomposition – modeling, algorithms, and parameter selection
    • Aujol J-F, Gilboa G, Chan T, Osher S. Structure-texture image decomposition – modeling, algorithms, and parameter selection. Int. J. Comput. Vis. 2006;67:111–136.
    • (2006) Int. J. Comput. Vis , vol.67 , pp. 111-136
    • Aujol, J.-F.1    Gilboa, G.2    Chan, T.3    Osher, S.4
  • 17
    • 0036538286 scopus 로고    scopus 로고
    • Iterative oblique projection onto convex sets and the split feasibility problem
    • Byrne CL. Iterative oblique projection onto convex sets and the split feasibility problem. Inverse Prob. 2002;18:441–453.
    • (2002) Inverse Prob , vol.18 , pp. 441-453
    • Byrne, C.L.1
  • 18
    • 0031492191 scopus 로고    scopus 로고
    • Image recovery via total variation minimization and related problems
    • Chambolle A, Lions PL. Image recovery via total variation minimization and related problems. Numer. Math. 1997;76:167–188.
    • (1997) Numer. Math , vol.76 , pp. 167-188
    • Chambolle, A.1    Lions, P.L.2
  • 19
    • 7044231546 scopus 로고    scopus 로고
    • An iterative thresholding algorithm for linear inverse problems with a sparsity constraint
    • Daubechies I, Defrise M, De Mol C. An iterative thresholding algorithm for linear inverse problems with a sparsity constraint. Comm. Pure Appl. Math. 2004;57:1413–1457.
    • (2004) Comm. Pure Appl. Math , vol.57 , pp. 1413-1457
    • Daubechies, I.1    Defrise, M.2    De Mol, C.3
  • 20
    • 84880683689 scopus 로고
    • Iteration methods for convexly constrained ill-posed problems in Hilbert space
    • Eicke B. Iteration methods for convexly constrained ill-posed problems in Hilbert space. Numer. Funct. Anal. Optim. 1992;13:413–429.
    • (1992) Numer. Funct. Anal. Optim , vol.13 , pp. 413-429
    • Eicke, B.1
  • 21
    • 0032166840 scopus 로고    scopus 로고
    • Convexly constrained linear inverse problems: iterative least-squares and regularization
    • Sabharwal A, Potter LC. Convexly constrained linear inverse problems: iterative least-squares and regularization. IEEE Trans. Signal Process. 1998;46:2345–2352.
    • (1998) IEEE Trans. Signal Process , vol.46 , pp. 2345-2352
    • Sabharwal, A.1    Potter, L.C.2
  • 26
    • 0000050153 scopus 로고
    • Projection methods for variational inequalities with application to the traffic assignment problem
    • Bertsekas DP, Gafni EM. Projection methods for variational inequalities with application to the traffic assignment problem. Math. Program. Stud. 1982;17:139–159.
    • (1982) Math. Program. Stud , vol.17 , pp. 139-159
    • Bertsekas, D.P.1    Gafni, E.M.2
  • 27
    • 0002230195 scopus 로고    scopus 로고
    • The primal Douglas–Rachford splitting algorithm for a class of monotone mappings with applications to the traffic equilibrium problem
    • Fukushima M. The primal Douglas–Rachford splitting algorithm for a class of monotone mappings with applications to the traffic equilibrium problem. Math. Program. 1996;72:1–15.
    • (1996) Math. Program , vol.72 , pp. 1-15
    • Fukushima, M.1
  • 30
    • 13244295576 scopus 로고    scopus 로고
    • Solving monotone inclusions via compositions of nonexpansive averaged operators
    • Combettes PL. Solving monotone inclusions via compositions of nonexpansive averaged operators. Optimization. 2004;53:475–504.
    • (2004) Optimization , vol.53 , pp. 475-504
    • Combettes, P.L.1
  • 31
    • 0000120615 scopus 로고
    • Ergodic convergence to a zero of the sum of monotone operators in Hilbert space
    • Passty GB. Ergodic convergence to a zero of the sum of monotone operators in Hilbert space. J. Math. Anal. Appl. 1979;72:383–390.
    • (1979) J. Math. Anal. Appl , vol.72 , pp. 383-390
    • Passty, G.B.1
  • 32
    • 84855933316 scopus 로고    scopus 로고
    • A monotone+skew splitting model for composite monotone inclusions in duality
    • Briceño-Arias LM, Combettes PL. A monotone+skew splitting model for composite monotone inclusions in duality. SIAM J. Optim. 2011;21:1230–1250.
    • (2011) SIAM J. Optim , vol.21 , pp. 1230-1250
    • Briceño-Arias, L.M.1    Combettes, P.L.2
  • 33
    • 73349126993 scopus 로고    scopus 로고
    • Iterative construction of the resolvent of a sum of maximal monotone operators
    • Combettes PL. Iterative construction of the resolvent of a sum of maximal monotone operators. J. Convex Anal. 2009;16:727–748.
    • (2009) J. Convex Anal , vol.16 , pp. 727-748
    • Combettes, P.L.1
  • 34
    • 84869774172 scopus 로고    scopus 로고
    • Primal-dual splitting algorithm for solving inclusions with mixtures of composite, Lipschitzian, and parallel-sum type monotone operators
    • Combettes PL, Pesquet J-C. Primal-dual splitting algorithm for solving inclusions with mixtures of composite, Lipschitzian, and parallel-sum type monotone operators. Set-Valued Var. Anal. 2012;20:307–330.
    • (2012) Set-Valued Var. Anal , vol.20 , pp. 307-330
    • Combettes, P.L.1    Pesquet, J.-C.2
  • 35
    • 84875493148 scopus 로고    scopus 로고
    • A splitting algorithm for dual monotone inclusions involving cocoercive operators
    • Vũ BC. A splitting algorithm for dual monotone inclusions involving cocoercive operators. Adv. Comput. Math. 2013;38:667–681.
    • (2013) Adv. Comput. Math , vol.38 , pp. 667-681
    • Vũ, B.C.1
  • 36
    • 79952292218 scopus 로고    scopus 로고
    • On weak convergence of the Douglas–Rachford method
    • Svaiter BF. On weak convergence of the Douglas–Rachford method. SIAM J. Control Optim. 2011;49:280–287.
    • (2011) SIAM J. Control Optim , vol.49 , pp. 280-287
    • Svaiter, B.F.1
  • 39
    • 0001188942 scopus 로고
    • Two remarks on the method of successive approximations
    • Krasnosel’skiĭ MA. Two remarks on the method of successive approximations. Uspehi Mat. Nauk (N.S.). 1955;10:123–127.
    • (1955) Uspehi Mat. Nauk (N.S.) , vol.10 , pp. 123-127
    • Krasnosel’skiĭ, M.A.1
  • 40
    • 84968518052 scopus 로고
    • Mean value methods in iteration
    • Mann WR. Mean value methods in iteration. Proc. Am. Math. Soc. 1953;4:506–510.
    • (1953) Proc. Am. Math. Soc , vol.4 , pp. 506-510
    • Mann, W.R.1
  • 41
    • 77956655101 scopus 로고    scopus 로고
    • Quasi–Fejérian analysis of some optimization algorithms
    • Butnariu D, Censor Y, Reich S, (eds), Amsterdam: Elsevier
    • Combettes PL. Quasi–Fejérian analysis of some optimization algorithms. In: Butnariu D, Censor Y, Reich S, editors. Inherently parallel algorithms for feasibility and optimization. Amsterdam: Elsevier; 2001. p. 115–152.
    • (2001) Inherently parallel algorithms for feasibility and optimization , pp. 115-152
    • Combettes, P.L.1
  • 43
  • 44
    • 78651107831 scopus 로고    scopus 로고
    • Convex variational formulation with smooth coupling for multicomponent signal decomposition and recovery
    • Briceño-Arias LM, Combettes PL. Convex variational formulation with smooth coupling for multicomponent signal decomposition and recovery. Numer. Math. Theory Methods Appl. 2009;2:485–508.
    • (2009) Numer. Math. Theory Methods Appl , vol.2 , pp. 485-508
    • Briceño-Arias, L.M.1    Combettes, P.L.2
  • 46
    • 0039279366 scopus 로고
    • Quelques propriétés des opérateurs angle-bornés et n-cycliquement monotones
    • Baillon J-B, Haddad G. Quelques propriétés des opérateurs angle-bornés et n-cycliquement monotones. Israel J. Math. 1977;26:137–150.
    • (1977) Israel J. Math , vol.26 , pp. 137-150
    • Baillon, J.-B.1    Haddad, G.2
  • 47
    • 78149327605 scopus 로고    scopus 로고
    • The Baillon–Haddad theorem revisited
    • Bauschke HH, Combettes PL. The Baillon–Haddad theorem revisited. J. Convex Anal. 2010;17:781–787.
    • (2010) J. Convex Anal , vol.17 , pp. 781-787
    • Bauschke, H.H.1    Combettes, P.L.2
  • 48
    • 84875502140 scopus 로고    scopus 로고
    • A generic first-order primal-dual method for convex optimization involving Lipschitzian, proximable and linear composite terms
    • Condat L. A generic first-order primal-dual method for convex optimization involving Lipschitzian, proximable and linear composite terms. Available from: http://hal.archives-ouvertes.fr/hal-00609728/en/.
    • Condat, L.1


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