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Volumn 6, Issue 2, 2013, Pages 938-983

A bilevel optimization approach for parameter learning in variational models

Author keywords

Bilevel optimization; Image denoising; Learning theory; Nondifferentiable optimization; Regularization parameter; Semismooth Newton algorithm

Indexed keywords

BI-LEVEL OPTIMIZATION; LEARNING THEORY; NON-DIFFERENTIABLE OPTIMIZATION; REGULARIZATION PARAMETERS; SEMISMOOTH NEWTON ALGORITHM;

EID: 84879933290     PISSN: None     EISSN: 19364954     Source Type: Journal    
DOI: 10.1137/120882706     Document Type: Article
Times cited : (211)

References (33)
  • 2
    • 0003496901 scopus 로고    scopus 로고
    • Kluwer Academic Publishers, Dordrecht, The Netherlands
    • J. Bard, Practical Bilevel Optimization, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1998.
    • (1998) Practical Bilevel Optimization
    • Bard, J.1
  • 3
    • 0031492191 scopus 로고    scopus 로고
    • Image recovery via total variation minimization and related problems
    • A. Chambolle and P.-L. Lions, Image recovery via total variation minimization and related problems, Numer. Math., 76 (1997), pp. 167-188.
    • (1997) Numer. Math , vol.76 , pp. 167-188
    • Chambolle, A.1    Lions, P.-L.2
  • 4
    • 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 (2010), pp. 120-145.
    • (2010) J. Math. Imaging Vision , vol.40 , pp. 120-145
    • Chambolle, A.1    Pock, T.2
  • 5
    • 0033295350 scopus 로고    scopus 로고
    • A nonlinear primal-dual method for total variation-based image restoration
    • T. F. Chan, G. H. Golub, and P. Mulet, A nonlinear primal-dual method for total variation-based image restoration, SIAM J. Sci. Comput., 20 (1999), pp. 1964-1977.
    • (1999) SIAM J. Sci. Comput , vol.20 , pp. 1964-1977
    • Chan, T.F.1    Golub, G.H.2    Mulet, P.3
  • 6
    • 0023382163 scopus 로고
    • Second-order necessary conditions in constrained semismooth optimization
    • R. W. Chaney, Second-order necessary conditions in constrained semismooth optimization, SIAM J. Control Optim., 25 (1987), pp. 1072-1081.
    • (1987) SIAM J. Control Optim , vol.25 , pp. 1072-1081
    • Chaney, R.W.1
  • 9
    • 80052712274 scopus 로고    scopus 로고
    • Optimal control of a class of variational inequalities of the second kind
    • J. C. De los Reyes, Optimal control of a class of variational inequalities of the second kind., SIAM J. Control Optim., 49 (2011), pp. 1629-1658.
    • (2011) SIAM J. Control Optim , vol.49 , pp. 1629-1658
    • De los Reyes, J.C.1
  • 11
    • 33751379736 scopus 로고    scopus 로고
    • Image denoising via sparse and redundant representations over learned dictionaries
    • M. Elad and M. Aharon, Image denoising via sparse and redundant representations over learned dictionaries, IEEE Trans. Image Process., 15 (2006), pp. 3736-3745.
    • (2006) IEEE Trans. Image Process , vol.15 , pp. 3736-3745
    • Elad, M.1    Aharon, M.2
  • 12
    • 0003277393 scopus 로고    scopus 로고
    • Regularization of Inverse Problems
    • Kluwer Academic Publishers, Dordrecht, The Netherlands
    • H. W. Engl, M. Hanke, and A. Neubauer, Regularization of Inverse Problems, Math. Appl. 375, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1996.
    • (1996) Math. Appl , vol.375
    • Engl, H.W.1    Hanke, M.2    Neubauer, A.3
  • 14
    • 77950679349 scopus 로고    scopus 로고
    • An infeasible primal-dual algorithm for total bounded variation-based inf-convolution-type image restoration
    • M. Hintermüller and G. Stadler, An infeasible primal-dual algorithm for total bounded variation-based inf-convolution-type image restoration, S IAM J. Sci. Comput., 28 (2006), pp. 1-23.
    • (2006) S IAM J. Sci. Comput , vol.28 , pp. 1-23
    • Hintermüller, M.1    Stadler, G.2
  • 16
    • 0034370334 scopus 로고    scopus 로고
    • Newton's method for a class of weakly singular optimal control problems
    • K. Ito and K. Kunisch, Newton's method for a class of weakly singular optimal control problems, SIAM J. Optim., 10 (2000), pp. 896-916.
    • (2000) SIAM J. Optim , vol.10 , pp. 896-916
    • Ito, K.1    Kunisch, K.2
  • 20
    • 33646887390 scopus 로고
    • On the limited memory BFGS method for large scale optimization
    • D. C. Liu and J. Nocedal, On the limited memory BFGS method for large scale optimization, Math. Programming, 45 (1989), pp. 503-528.
    • (1989) Math. Programming , vol.45 , pp. 503-528
    • Liu, D.C.1    Nocedal, J.2
  • 23
    • 0033677038 scopus 로고    scopus 로고
    • A generalized mathematical program with equilibrium constraints
    • J. V. Outrata, A generalized mathematical program with equilibrium constraints, SIAM J. Control Optim., 38 (2000), p. 1623-1638.
    • (2000) SIAM J. Control Optim , vol.38 , pp. 1623-1638
    • Outrata, J.V.1
  • 32
    • 0001556589 scopus 로고    scopus 로고
    • Iterative methods for total variation denoising
    • C. R. Vogel and M. E. Oman, Iterative methods for total variation denoising, SIAM J. Sci. Comput., 17 (1996), pp. 227-238.
    • (1996) SIAM J. Sci. Comput , vol.1 , pp. 227-238
    • Vogel, C.R.1    Oman, M.E.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.