[1]
|
J. Baptiste, H. Urruty and C. Lemaéchal, Convex Analysis and Minimization Algorithms, Springer, Berlin, 1993.
|
[2]
|
F. H. Clarke, Yu. S. Ledyaev, R. J. Stern and P. R. Wolenski, Nonsmooth Analysis and Control Theory, Springer, New York, 1998.
|
[3]
|
R. Correa and C. Lemaréchal, Convergence of some algorithms for convex minimization, Math. Program., 62 (1993), 261-275.
doi: 10.1007/BF01585170.
|
[4]
|
Z. Fu, K. Ren, J. Shu, X. Sun and F. Huang, Enabling personalized search over encrypted out-sourced data with efficiency improvement, IEEE Transactions on Parallel and Distributed Systems, (2015).
|
[5]
|
B. Gu, V. S. Sheng, K. Y. Tay, W. Romano and S. Li, Incremental support vector learning for ordinal regression, IEEE Transactions on Neural Networks and Learning Systems, 26 (2015), 1403-1416.
doi: 10.1109/TNNLS.2014.2342533.
|
[6]
|
B. Gu and V. S. Sheng, A robust regularization path algorithm for ν-support vector classification, IEEE Transactions on Neural Networks and Learning Systems, 28 (2017), 1241-1248.
doi: 10.1109/TNNLS.2016.2527796.
|
[7]
|
J. Gu, X. Xiao and L. Zhang, A subgradient-based convex approximations method for DC programming and its applications, Journal of Industrial Management Optimization, 12 (2016), 1349-1366.
doi: 10.3934/jimo.2016.12.1349.
|
[8]
|
K. C. Kiwiel, Methods of Descent for Nondifferentiable Optimization, Lectures Notes in Mathematics, Springer, Berlin, 1985.
|
[9]
|
K. C. Kiwiel, Proximity control in bundle methods for convex nondifferentiable minimization, Math. Program., 46 (1990), 105-122.
doi: 10.1007/BF01585731.
|
[10]
|
K. C. Kiwiel, Efficiency of the analytic center cutting plane method for convex minimization, SIAM J. Optim., 7 (1997), 336-346.
doi: 10.1137/S1052623494275768.
|
[11]
|
K. C. Kiwiel, The efficiency of subgradient projection methods for convex optimization. Part 1: General level methods, SIAM Journal on Control and Optimization, 34 (1996), 660-676.
doi: 10.1137/0334031.
|
[12]
|
K. C. Kiwiel, T. Larsson and P. O. Lindberg, The efficiency of ball step subgradient level methods for convex optimization, Mathematics of Operations Research, 24 (1999), 237-254.
doi: 10.1287/moor.24.1.237.
|
[13]
|
K. C. Kiwiel, Efficiency of proximal bundle methods, Journal of Optimization Theory and Applications, 104 (2000), 589-603.
doi: 10.1023/A:1004689609425.
|
[14]
|
J. Li, X. Li, B. Yang and X. Sun, Segmentation-based image copy-move forgery detection scheme, IEEE Transactions on Information Forensics and Security, 10 (2015), 507-518.
|
[15]
|
E. S. Mistakidis and G. E. Stavroulakis, Nonconvex Optimization in Mechanics. Smooth and Nonsmooth Algorithms, Heuristics and Engineering Applications, F. E. M. Kluwer Academic Publisher, Dordrecht, 1998.
|
[16]
|
J. J. Moreau, P. D. Panagiotopoulos and G. Strang (Eds. ), Topics in Nonsmooth Mechanics, Birkhäuser Verlag, Basel, 1988.
|
[17]
|
A. Ouorou, A proximal cutting plane method using Chebychev center for nonsmooth convex optimization, Math. Program. Ser. A, 119 (2009), 239-271.
doi: 10.1007/s10107-008-0209-x.
|
[18]
|
J. Outrata, M. KoÄvara and J. Zowe, Nonsmooth Approach to Optimization Problems With Equilibrium Constraints. Theory, Applications and Numerical Results, Kluwer Academic Publishers, Dordrecht, 1998.
|
[19]
|
Z. Pan, Y. Zhang and S. Kwong, Efficient motion and disparity estimation optimization for low complexity multiview video coding, IEEE Transactions on Broadcasting, 61 (2015), 166-176.
|
[20]
|
H. Schramm and J. Zowe, A version of the bundle idea for minimizing a nonsmooth function: Conceptual idea, convergence analysis, numerical results, SIAM J. Optim., 2 (1992), 121-152.
doi: 10.1137/0802008.
|
[21]
|
J. Shen, D. Li and L. Pang, A cutting plane and level stabilization bundle method with inexact data for minimizing nonsmooth nonconvex functions, Abstract and Applied Analysis, 2014 (2014), Article ID 192893, 6pp.
|
[22]
|
J. Shen and L. Pang, An approximate bundle-type auxiliary problem method for generalized variational inequality, Mathematical and Computer Modeling, 48 (2008), 769-775.
doi: 10.1016/j.mcm.2007.11.005.
|
[23]
|
J. Shen, X. Liu, F. Guo and S. Wang, An approximate redistributed proximal bundle method with inexact data for minimizing nonsmooth nonconvex functions, Mathematical Problems in Engineering, 2015 (2015), Article ID 215310, 9pp.
|
[24]
|
J. Shen, Z. Xia and L. Pang, A proximal bundle method with inexact data for convex nondifferentiable minimization, Nonlinear Analysis A : theory, method and applications, 66 (2007), 2016-2027.
doi: 10.1016/j.na.2006.02.039.
|
[25]
|
K. Wang, L. Xu and D. Han, A new parallel splitting descent method for structured variational inequalities, Journal of Industrial Management Optimization, 10 (2014), 461-476.
|
[26]
|
Z. Xia, X. Wang, X. Sun and Q. Wang, A secure and dynamic multi-keyword ranked search scheme over encrypted cloud data, IEEE Transactions on Parallel and Distributed Systems, 27 (2016), 340-352.
doi: 10.1109/TPDS.2015.2401003.
|
[27]
|
G. Yuan, Z. Wei and G. Li, A modified Polak-Ribiére-Polyak conjugate gradient algorithm for nonsmooth convex programs, Journal of Computational and Applied Mathematics, 255 (2014), 86-96.
doi: 10.1016/j.cam.2013.04.032.
|
[28]
|
G. Yuan, Z. Meng and Y. Li, A modified Hestenes and Stiefel conjugate gradient algorithm for large-scale nonsmooth minimizations and nonlinear equations, Journal of Optimization Theory and Applications, 168 (2016), 129-152.
doi: 10.1007/s10957-015-0781-1.
|
[29]
|
G. Yuan and M. Zhang, A three-terms Polak-Ribiére-Polyak conjugate gradient algorithm for large-scale nonlinear equations, Journal of Computational and Applied Mathematics, 286 (2015), 186-195.
doi: 10.1016/j.cam.2015.03.014.
|
[30]
|
J. Zhang, Y. Li and L. Zhang, On the coderivative of the solution mapping to a second-order cone constrained parametric variational inequality, Journal of Global Optimization, 61 (2015), 379-396.
doi: 10.1007/s10898-014-0181-3.
|
[31]
|
J. Zhang, S. Lin and L. Zhang, A log-exponential regularization method for a mathmatical program with general vertical complementarity constraints, Journal of Industrial Management Optimization, 9 (2013), 561-577.
doi: 10.3934/jimo.2013.9.561.
|