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Volumn 47, Issue 3, 2013, Pages 231-238

Prox-regularity of rank constraint sets and implications for algorithms

Author keywords

Constraint qualification; Linear convergence; Method of alternating projections; Normal cone; Projection operator; Prox regular; Rank constraint; Rank optimization; Sparsity; Superregularity

Indexed keywords

CONSTRAINT QUALIFICATION; LINEAR CONVERGENCE; METHOD OF ALTERNATING PROJECTIONS; NORMAL CONES; PROJECTION OPERATOR; PROX-REGULAR; RANK CONSTRAINTS; SPARSITY; SUPERREGULARITY;

EID: 84883255319     PISSN: 09249907     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10851-012-0406-3     Document Type: Article
Times cited : (39)

References (24)
  • 1
    • 0001386281 scopus 로고
    • On matrices depending on parameters. Translation from Usp
    • Arnol'd, V.I.: On matrices depending on parameters. Translation from Usp. Mat. Nauk 26, No. 2(158), 101-114 (1971)
    • (1971) Mat. Nauk , vol.26 , Issue.2-158 , pp. 101-114
    • Arnol'D, V.I.1
  • 2
    • 77953092582 scopus 로고    scopus 로고
    • Proximal alternating minimization and projection methods for nonconvex problems: An approach based on the Kurdyka-Lojasiewicz inequality
    • 2674728 1214.65036 10.1287/moor.1100.0449
    • Attouch, H.; Bolte, J.; Redont, P.; Soubeyran, A.: Proximal alternating minimization and projection methods for nonconvex problems: an approach based on the Kurdyka-Lojasiewicz inequality. Math. Oper. Res. 35(2), 438-457 (2010)
    • (2010) Math. Oper. Res. , vol.35 , Issue.2 , pp. 438-457
    • Attouch, H.1    Bolte, J.2    Redont, P.3    Soubeyran, A.4
  • 5
    • 84976509864 scopus 로고    scopus 로고
    • A linearly convergent algorithm for solving a class of nonconvex/affine feasibility problems
    • H. Bauschke R. Burachick Combettes V. Elser D.R. Luke H. Wolkowicz (eds) Springer Berlin 10.1007/978-1-4419-9569-8-3
    • Beck, A.; Teboulle, M.: A linearly convergent algorithm for solving a class of nonconvex/affine feasibility problems. In: Bauschke, H.; Burachick, R.; Combettes, P.; Elser, V.; Luke, D.R.; Wolkowicz, H. (eds.) Fixed-Point Algorithms for Inverse Problems in Science and Engineering, pp. 33-48. Springer, Berlin (2011)
    • (2011) Fixed-Point Algorithms for Inverse Problems in Science and Engineering , pp. 33-48
    • Beck, A.1    Teboulle, M.2
  • 6
    • 0025535641 scopus 로고
    • Method of successive projections for finding a common point of sets in metric spaces
    • 1084685 0696.90052 10.1007/BF00939646
    • Combettes, P.L.; Trussell, H.J.: Method of successive projections for finding a common point of sets in metric spaces. J. Optim. Theory Appl. 67(3), 487-507 (1990)
    • (1990) J. Optim. Theory Appl. , vol.67 , Issue.3 , pp. 487-507
    • Combettes, P.L.1    Trussell, H.J.2
  • 7
    • 84968469617 scopus 로고
    • Curvature measures
    • 110078 0089.38402 10.1090/S0002-9947-1959-0110078-1
    • Federer, H.: Curvature measures. Trans. Am. Math. Soc. 93, 418-491 (1959)
    • (1959) Trans. Am. Math. Soc. , vol.93 , pp. 418-491
    • Federer, H.1
  • 8
    • 84879693654 scopus 로고    scopus 로고
    • When only global optimization matters
    • 10.1007/s10898-011-9826-7
    • Hiriart-Urruty, J.-B.: When only global optimization matters. J. Glob. Optim. (2012). doi: 10.1007/s10898-011-9826-7
    • (2012) J. Glob. Optim.
    • Hiriart-Urruty, J.-B.1
  • 9
    • 0004151494 scopus 로고
    • Cambridge University Press New York 0576.15001 10.1017/CBO9780511810817
    • Horn, R.A.; Johnson, C.R.: Matrix Analysis. Cambridge University Press, New York (1985)
    • (1985) Matrix Analysis
    • Horn, R.A.1    Johnson, C.R.2
  • 10
    • 33744931869 scopus 로고    scopus 로고
    • Stationarity and regularity of set systems
    • 2148023 1105.90104
    • Kruger, A.Y.: Stationarity and regularity of set systems. Pac. J. Optim. 1(1), 101-126 (2005)
    • (2005) Pac. J. Optim. , vol.1 , Issue.1 , pp. 101-126
    • Kruger, A.Y.1
  • 11
    • 84875475455 scopus 로고    scopus 로고
    • Generalized subdifferentials of the rank function
    • 10.1007/s11590-012-0456-x
    • Le, H.Y.: Generalized subdifferentials of the rank function. Optim. Lett. (2012). doi: 10.1007/s11590-012-0456-x
    • (2012) Optim. Lett.
    • Le, H.Y.1
  • 12
    • 84883247151 scopus 로고    scopus 로고
    • Eigenvalues and nonsmooth optimization
    • L.M. Pardo (eds) et al. Santander Selected papers based on the presentations at the International Conference of the Foundations of Computational Mathematics (FoCM), Santander, Spain, June 30-July 9, 2005. Cambridge: Cambridge University Press. London Mathematical Society Lecture Note Series, 331, 208-229 (2006)
    • Lewis, A.S.: Eigenvalues and nonsmooth optimization. In: Pardo, L.M.; et al. (eds.) Foundations of Computational Mathematics, Santander (2005). Selected papers based on the presentations at the International Conference of the Foundations of Computational Mathematics (FoCM), Santander, Spain, June 30-July 9, 2005. Cambridge: Cambridge University Press. London Mathematical Society Lecture Note Series, vol. 331, pp. 208-229 (2006)
    • (2005) Foundations of Computational Mathematics
    • Lewis, A.S.1
  • 13
    • 70349387487 scopus 로고    scopus 로고
    • Local linear convergence of alternating and averaged projections
    • 2519868 1169.49030 10.1007/s10208-008-9036-y
    • Lewis, A.S.; Luke, D.R.; Malick, J.: Local linear convergence of alternating and averaged projections. Found. Comput. Math. 9(4), 485-513 (2009)
    • (2009) Found. Comput. Math. , vol.9 , Issue.4 , pp. 485-513
    • Lewis, A.S.1    Luke, D.R.2    Malick, J.3
  • 14
    • 48549094732 scopus 로고    scopus 로고
    • Alternating projections on manifolds
    • 2393548 1163.65040 10.1287/moor.1070.0291
    • Lewis, A.S.; Malick, J.: Alternating projections on manifolds. Math. Oper. Res. 33, 216-234 (2008)
    • (2008) Math. Oper. Res. , vol.33 , pp. 216-234
    • Lewis, A.S.1    Malick, J.2
  • 15
    • 22044456250 scopus 로고    scopus 로고
    • Nonsmooth analysis of singular values. I: Theory
    • 2162512 1129.49025 10.1007/s11228-004-7197-7
    • Lewis, A.S.; Sendov, H.S.: Nonsmooth analysis of singular values. I: Theory. Set-Valued Anal. 13(3), 213-241 (2005)
    • (2005) Set-Valued Anal. , vol.13 , Issue.3 , pp. 213-241
    • Lewis, A.S.1    Sendov, H.S.2
  • 16
    • 22044453362 scopus 로고    scopus 로고
    • Nonsmooth analysis of singular values. II: Applications
    • 2162513 1129.49026 10.1007/s11228-004-7198-6
    • Lewis, A.S.; Sendov, H.S.: Nonsmooth analysis of singular values. II: Applications. Set-Valued Anal. 13(3), 243-264 (2005)
    • (2005) Set-Valued Anal. , vol.13 , Issue.3 , pp. 243-264
    • Lewis, A.S.1    Sendov, H.S.2
  • 17
    • 82155167605 scopus 로고    scopus 로고
    • Local linear convergence of approximate projections onto regularized sets
    • 2861355 1236.49072 10.1016/j.na.2011.08.027
    • Luke, D.R.: Local linear convergence of approximate projections onto regularized sets. Nonlinear Anal. 75, 1531-1546 (2012)
    • (2012) Nonlinear Anal. , vol.75 , pp. 1531-1546
    • Luke, D.R.1
  • 18
    • 0006503785 scopus 로고
    • Nonsmooth analysis with nonconvex generalized differentials and adjoint mappings
    • 771737 0557.49007 Russian
    • Mordukhovich, B.S.: Nonsmooth analysis with nonconvex generalized differentials and adjoint mappings. Dokl. Akad. Nauk BSSR 28, 976-979 (1984). Russian
    • (1984) Dokl. Akad. Nauk BSSR , vol.28 , pp. 976-979
    • Mordukhovich, B.S.1
  • 20
    • 37549062277 scopus 로고    scopus 로고
    • The charge flipping algorithm
    • 10.1107/S0108767307046028
    • Oszlányi, G.; Sütó, A.: The charge flipping algorithm. Acta Crystalogr. A 64, 123-134 (2008)
    • (2008) Acta Crystalogr. A , vol.64 , pp. 123-134
    • Oszlányi, G.1    Sütó, A.2
  • 22
    • 23044523810 scopus 로고    scopus 로고
    • Local differentiability of distance functions
    • 1694378 0960.49018 10.1090/S0002-9947-00-02550-2
    • Poliquin, R.A.; Rockafellar, R.T.; Thibault, L.: Local differentiability of distance functions. Trans. Am. Math. Soc. 352(11), 5231-5249 (2000)
    • (2000) Trans. Am. Math. Soc. , vol.352 , Issue.11 , pp. 5231-5249
    • Poliquin, R.A.1    Rockafellar, R.T.2    Thibault, L.3
  • 23
    • 78549288866 scopus 로고    scopus 로고
    • Guaranteed minimum rank solutions of matrix equations via nuclear norm minimization
    • 2680543 1198.90321 10.1137/070697835
    • Recht, B.; Fazel, M.; Parrilo, P.: Guaranteed minimum rank solutions of matrix equations via nuclear norm minimization. SIAM Rev. 52(3), 471-501 (2010)
    • (2010) SIAM Rev. , vol.52 , Issue.3 , pp. 471-501
    • Recht, B.1    Fazel, M.2    Parrilo, P.3
  • 24
    • 0004258516 scopus 로고    scopus 로고
    • Grundlehren der mathematischen Wissenschaften Springer Berlin 0888.49001 10.1007/978-3-642-02431-3
    • Rockafellar, R.T.; Wets, R.J.: Variational Analysis. Grundlehren der mathematischen Wissenschaften. Springer, Berlin (1998)
    • (1998) Variational Analysis
    • Rockafellar, R.T.1    Wets, R.J.2


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