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An alternating linearization method with inexact data for bilevel nonsmooth convex optimization
1. | School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, Liaoning, China, China, China, China |
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D. P. Bertsekas, Convex Analysis and Optimization, With Angelia Nedić and Asuman E. Ozdaglar, Athena Scientific, Belmont, MA, 2003. |
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M. Hintermüller, A proximal bundle method based on approximate subgradients, Computational Optimization and Applications, 20 (2001), 245-266.
doi: 10.1023/A:1011259017643. |
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K. C. Kiwiel, Approximations in proximal bundle methods and decomposition of convex programs, J. Optim. Theory Appl., 84 (1995), 529-548.
doi: 10.1007/BF02191984. |
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K. C. Kiwiel, C. H. Rosa and A. Ruszczyński, Proximal decomposition via alternating linearization, SIAM J. Optimization, 9 (1999), 668-689.
doi: 10.1137/S1052623495288064. |
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C. Lemaréchal and C. Sagastizábal, Practical aspects of the Moreau-Yosida regularization: Theoretical preliminaries, SIAM J. Optim., 7 (1997), 367-385.
doi: 10.1137/S1052623494267127. |
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O. L. Mangasarian, Sufficiency of exact penalty minimization, SIAM Journal on Control and Optimization, 23 (1985), 30-37.
doi: 10.1137/0323003. |
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M. M. Mäkelä and P. Neittaanmäki, Nonsmooth Optimization: Analysis and Algorithms with Applications to Optimal Control, World Scientific Publishing Co., Inc., River Edge, New Jersey, 1992. |
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R. T. Rockafellar, Convex Analysis, Princeton Mathematical Series, No. 28, Princeton University Press, Princeton, New Jersey, 1970. |
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R. T. Rockafellar, Monotone operators and the proximal point algorithm, SIAM. Control Optim., 14 (1976), 877-898.
doi: 10.1137/0314056. |
[12] |
R. T. Rockafellar and R. J. -B. Wets, Variational Analysis, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 317, Springer-Verlag, Berlin, 1998.
doi: 10.1007/978-3-642-02431-3. |
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M. V. Solodov, A bundle method for a class of bilevel nonsmooth convex minimization problems, SIAM J. Optimization, 18 (2007), 242-259.
doi: 10.1137/050647566. |
show all references
References:
[1] |
D. P. Bertsekas, Convex Analysis and Optimization, With Angelia Nedić and Asuman E. Ozdaglar, Athena Scientific, Belmont, MA, 2003. |
[2] |
S. Dempe, Foundations of Bilevel Programming, Nonconvex Optimization and its Applications, 61, Kluwer Academic Publishers, Dordrecht, 2002. |
[3] |
M. Hintermüller, A proximal bundle method based on approximate subgradients, Computational Optimization and Applications, 20 (2001), 245-266.
doi: 10.1023/A:1011259017643. |
[4] |
K. C. Kiwiel, Methods of Descent for Nondifferentiable Optimization, Lecture Notes in Mathematics, 1133, Springer-Verlag, Berlin, 1985. |
[5] |
K. C. Kiwiel, Approximations in proximal bundle methods and decomposition of convex programs, J. Optim. Theory Appl., 84 (1995), 529-548.
doi: 10.1007/BF02191984. |
[6] |
K. C. Kiwiel, C. H. Rosa and A. Ruszczyński, Proximal decomposition via alternating linearization, SIAM J. Optimization, 9 (1999), 668-689.
doi: 10.1137/S1052623495288064. |
[7] |
C. Lemaréchal and C. Sagastizábal, Practical aspects of the Moreau-Yosida regularization: Theoretical preliminaries, SIAM J. Optim., 7 (1997), 367-385.
doi: 10.1137/S1052623494267127. |
[8] |
O. L. Mangasarian, Sufficiency of exact penalty minimization, SIAM Journal on Control and Optimization, 23 (1985), 30-37.
doi: 10.1137/0323003. |
[9] |
M. M. Mäkelä and P. Neittaanmäki, Nonsmooth Optimization: Analysis and Algorithms with Applications to Optimal Control, World Scientific Publishing Co., Inc., River Edge, New Jersey, 1992. |
[10] |
R. T. Rockafellar, Convex Analysis, Princeton Mathematical Series, No. 28, Princeton University Press, Princeton, New Jersey, 1970. |
[11] |
R. T. Rockafellar, Monotone operators and the proximal point algorithm, SIAM. Control Optim., 14 (1976), 877-898.
doi: 10.1137/0314056. |
[12] |
R. T. Rockafellar and R. J. -B. Wets, Variational Analysis, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 317, Springer-Verlag, Berlin, 1998.
doi: 10.1007/978-3-642-02431-3. |
[13] |
M. V. Solodov, A bundle method for a class of bilevel nonsmooth convex minimization problems, SIAM J. Optimization, 18 (2007), 242-259.
doi: 10.1137/050647566. |
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