A Decomposition Method with Redistributed Subroutine for Constrained Nonconvex Optimization

Abstract and Applied Analysis

Research Article

Dan Li²  Li-Ping Pang²  Wei Wang¹  Yuan Lu³ 

[1] School of Mathematical, Liaoning Normal University, Dalian 116029, China, lnnu.edu.cn;School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China, dlut.edu.cn;School of Sciences, Shenyang University, Shenyang 110044, China, syu.edu.cn

Others  :  1296843
DOI  :  10.1155/2013/376403

 received in 2012-09-06, accepted in 2012-12-13,  发布年份 2013

【 授权许可】

CC BY   
Copyright © 2013 Yuan Lu et al. 2013

【 参考文献 】

• [1]Y. Lu, L.-P. Pang, F.-F. Guo, Z.-Q. Xia. et al.(2010). A superlinear space decomposition algorithm for constrained nonsmooth convex program. Journal of Computational and Applied Mathematics.234(1):224-232. DOI: 10.1016/j.cam.2009.12.018.
• [2]C. Lemaréchal, F. Oustry, C. Sagastizábal. (2000). The -Lagrangian of a convex function. Transactions of the American Mathematical Society.352(2):711-729. DOI: 10.1016/j.cam.2009.12.018.
• [3]R. Mifflin, C. Sagastizábal. (1999). -decomposition derivatives for convex max-functions. Ill-Posed Variational Problems and Regularization Techniques.477:167-186. DOI: 10.1016/j.cam.2009.12.018.
• [4]C. Lemaréchal, C. Sagastizábal. (1996). More than first-order developments of convex functions: primal-dual relations. Journal of Convex Analysis.3(2):255-268. DOI: 10.1016/j.cam.2009.12.018.
• [5]R. Mifflin, C. Sagastizábal. (2000). On -theory for functions with primal-dual gradient structure. SIAM Journal on Optimization.11(2):547-571. DOI: 10.1016/j.cam.2009.12.018.
• [6]R. Mifflin, C. Sagastizábal. (2000). Functions with primal-dual gradient structure and -Hessians. Nonlinear Optimization and Related Topics.36:219-233. DOI: 10.1016/j.cam.2009.12.018.
• [7]R. Mifflin, C. Sagastizábal. (2003). Primal-dual gradient structured functions: second-order results; links to epi-derivatives and partly smooth functions. SIAM Journal on Optimization.13(4):1174-1194. DOI: 10.1016/j.cam.2009.12.018.
• [8]R. Mifflin, C. Sagastizábal. (2005). A -algorithm for convex minimization. Mathematical Programming B.104(2-3):583-608. DOI: 10.1016/j.cam.2009.12.018.
• [9]F. Shan, L.-P. Pang, L.-M. Zhu, Z.-Q. Xia. et al.(2008). A -decomposed method for solving an MPEC problem. Applied Mathematics and Mechanics.29(4):535-540. DOI: 10.1016/j.cam.2009.12.018.
• [10]Y. Lu, L.-P. Pang, J. Shen, X.-J. Liang. et al.(2012). A decomposition algorithm for convex nondifferentiable minimization with errors. Journal of Applied Mathematics.2012-15. DOI: 10.1016/j.cam.2009.12.018.
• [11]A. Daniilidis, C. Sagastizábal, M. Solodov. (2009). Identifying structure of nonsmooth convex functions by the bundle technique. SIAM Journal on Optimization.20(2):820-840. DOI: 10.1016/j.cam.2009.12.018.
• [12]W. L. Hare. (2009). A proximal method for identifying active manifolds. Computational Optimization and Applications.43(2):295-306. DOI: 10.1016/j.cam.2009.12.018.
• [13]W. L. Hare. (2006). Functions and sets of smooth substructure: relationships and examples. Computational Optimization and Applications.33(2-3):249-270. DOI: 10.1016/j.cam.2009.12.018.
• [14]R. Mifflin, L. Qi, D. Sun. (1999). Properties of the Moreau-Yosida regularization of a piecewise convex function. Mathematical Programming A.84(2):269-281. DOI: 10.1016/j.cam.2009.12.018.
• [15]R. T. Rockafellar, R. J.-B. Wets. (1998). Variational Analysis.317. DOI: 10.1016/j.cam.2009.12.018.
• [16]R. Mifflin, C. Sagastizábal. (2004). -smoothness and proximal point results for some nonconvex functions. Optimization Methods & Software.19(5):463-478. DOI: 10.1016/j.cam.2009.12.018.
• [17]S. Lang. (1993). Real and Functional Analysis. DOI: 10.1016/j.cam.2009.12.018.
• [18]W. Hare, C. Sagastizábal. (2009). Computing proximal points of nonconvex functions. Mathematical Programming B.116(1-2):221-258. DOI: 10.1016/j.cam.2009.12.018.
• [19]W. L. Hare, C. Sagastizábal. (2010). A redistributed proximal bundle method for nonconvex optimization. SIAM Journal on Optimization.20(5):2442-2473. DOI: 10.1016/j.cam.2009.12.018.