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Single machine batch scheduling problem to minimize makespan with controllable setup and jobs processing times
Proximal iterative Gaussian smoothing algorithm for a class of nonsmooth convex minimization problems
1. | Department of Mathematics and Physics, Shanghai Dianji University, 1350 Ganlan Road, Shanghai, 201306, China |
2. | School of Electrical Engineering, Shanghai Dianji University, 1350 Ganlan Road, Shanghai, 201306, China |
3. | School of Mathematics and Information Science, Shandong Institute of Business and Technology, 191 Binhaizhong Road, Yantan, Shandong Province, 264005, China |
References:
[1] |
H. H. Bauschke and P. L. Combettes, Convex Analysis and Monotone Operator Theory in Hilbert Spaces, CMS Books in Mathematics, Springer, 2011.
doi: 10.1007/978-1-4419-9467-7. |
[2] |
A. Beck and M. Teboulle, A fast iterative shrinkage-thresholding algorithm for linear inverse problems, SIAM Journal of Imaging Sciences, 2 (2009), 183-202.
doi: 10.1137/080716542. |
[3] |
D. P. Bertsekas, Nonlinear Programming, Athena Scientific, Belmont, 1999. |
[4] |
E. J. Candes, X. Li, Y. Ma and J. Wright, Robust principal component analysis, Journal of the Association for Computing Machinery, 58 (2011), 219-226.
doi: 10.1145/1970392.1970395. |
[5] |
J. Duchi and Y. Singer, Efficient online and batch learning using forward backward splitting, The Journal of Machine Learning Research, 10 (2009), 2899-2934. |
[6] |
Y. Nesterov, Introductory lectures on convex optimization: A basic course, Springer, 2004.
doi: 10.1007/978-1-4419-8853-9. |
[7] |
Y. Nesterov, Smooth minimization of non-smooth functions,, Mathematical Programming, 103 (): 127.
doi: 10.1007/s10107-004-0552-5. |
[8] |
Y. Nesterov, Random gradient-free minimization of convex functions, Core discussion paper, 2001, http://www.uclouvain.be/core. |
[9] |
R. T. Rockafellar, Convex Analysis, Princeton University Press, 1970. |
[10] |
M. J. Wainwright, P. Ravikumar and J. D. Lafferty, High-dimensional graphical model selection using l1-regularized logistic regression, In Advances in Neural Information Processing Systems,19 (2007),1465-1472. |
[11] |
M. Yuan and Y. Lin, Model selection and estimation in the Gaussian graphical model, Biometrika, 94 (2007), 19-35.
doi: 10.1093/biomet/asm018. |
[12] |
C. Zalinescu, Convex Analysis in General Vector Spaces, World Scientific, 2002.
doi: 10.1142/9789812777096. |
show all references
References:
[1] |
H. H. Bauschke and P. L. Combettes, Convex Analysis and Monotone Operator Theory in Hilbert Spaces, CMS Books in Mathematics, Springer, 2011.
doi: 10.1007/978-1-4419-9467-7. |
[2] |
A. Beck and M. Teboulle, A fast iterative shrinkage-thresholding algorithm for linear inverse problems, SIAM Journal of Imaging Sciences, 2 (2009), 183-202.
doi: 10.1137/080716542. |
[3] |
D. P. Bertsekas, Nonlinear Programming, Athena Scientific, Belmont, 1999. |
[4] |
E. J. Candes, X. Li, Y. Ma and J. Wright, Robust principal component analysis, Journal of the Association for Computing Machinery, 58 (2011), 219-226.
doi: 10.1145/1970392.1970395. |
[5] |
J. Duchi and Y. Singer, Efficient online and batch learning using forward backward splitting, The Journal of Machine Learning Research, 10 (2009), 2899-2934. |
[6] |
Y. Nesterov, Introductory lectures on convex optimization: A basic course, Springer, 2004.
doi: 10.1007/978-1-4419-8853-9. |
[7] |
Y. Nesterov, Smooth minimization of non-smooth functions,, Mathematical Programming, 103 (): 127.
doi: 10.1007/s10107-004-0552-5. |
[8] |
Y. Nesterov, Random gradient-free minimization of convex functions, Core discussion paper, 2001, http://www.uclouvain.be/core. |
[9] |
R. T. Rockafellar, Convex Analysis, Princeton University Press, 1970. |
[10] |
M. J. Wainwright, P. Ravikumar and J. D. Lafferty, High-dimensional graphical model selection using l1-regularized logistic regression, In Advances in Neural Information Processing Systems,19 (2007),1465-1472. |
[11] |
M. Yuan and Y. Lin, Model selection and estimation in the Gaussian graphical model, Biometrika, 94 (2007), 19-35.
doi: 10.1093/biomet/asm018. |
[12] |
C. Zalinescu, Convex Analysis in General Vector Spaces, World Scientific, 2002.
doi: 10.1142/9789812777096. |
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