求解一类非凸非光滑问题的惯性邻近交替极小化算法
Inertial Proximal Alternating Minimization Algorithm for a Class of Nonconvex and Nonsmooth Problems
DOI: 10.12677/AAM.2019.87142, PDF,    国家自然科学基金支持
作者: 陈梦霞, 郑海艳：广西大学数学与信息科学学院，广西 南宁
关键词: 非凸非光滑；Kurdyka-Lojasiewicz性质；惯性；交替极小化方法；Nonconvex and Nonsmooth； Kurdyka-Lojasiewicz Property； Inertial； Alternating Minimization Algorithm
摘要: 本文考虑一类非凸非光滑优化问题，提出了一种惯性邻近交替极小化算法。通过构造一个新的效益函数H，并保证其具有下降性，证明了算法的全局收敛性。当H为Kurdyka-Lojasiewicz函数时，证明了算法的强收敛性。
Abstract: In this paper, we propose an inertial proximal alternating minimization algorithm for a class of nonconvex and nonsmooth problems. We show the global convergence by constructing a new merit function H with guaranteed descent property. If H satisfies the Kurdyka-Lojasiewicz property, we determine the strongly convergence of the whole sequence.
文章引用：陈梦霞, 郑海艳. 求解一类非凸非光滑问题的惯性邻近交替极小化算法[J]. 应用数学进展, 2019, 8(7): 1228-1238. https://doi.org/10.12677/AAM.2019.87142

参考文献

[1] Bertsekas, D.P. and Tsitsiklis, J.N. (1989) Parallel and Distributed Computation: Numerical Methods (Vol. 23). Prentice Hall, Englewood Cliffs, NJ.
[2] Auslender, A. (1992) Asymptotic Properties of the Fenchel Dual Functional and Applications to Decomposition Problems. Journal of Optimization Theory and Applications, 73, 427-449. [Google Scholar] [CrossRef] 
[3] Alvarez, F. (2000) On the Minimizing Property of a Second Order Dis-sipative System in Hilbert Spaces. SIAM Journal on Control and Optimization, 38, 1102-1119. [Google Scholar] [CrossRef] 
[4] Ochs, P., Chen, Y., Brox, T. and & Pock, T. (2014) iPiano: In-ertial Proximal Algorithm for Nonconvex Optimization. SIAM Journal on Imaging Sciences, 7, 1388-1419. [Google Scholar] [CrossRef] 
[5] Ochs, P., Brox, T. and Pock, T. (2015) iPiasco: Inertial Proximal Algo-rithm for Strongly Convex Optimization. Journal of Mathematical Imaging and Vision, 53, 171-181. [Google Scholar] [CrossRef] 
[6] Boţ, R.I., Csetnek, E.R. and Hendrich, C. (2015) Inertial Doug-las-Rachford Splitting for Monotone Inclusion Problems. Applied Mathematics and Computation, 256, 472-487. [Google Scholar] [CrossRef] 
[7] Bot, R.I. and Csetnek, E.R. (2014) An Inertial Alternating Direction Method of Multipliers. Mathematics, ArXiv preprint arXiv: 1404.4582.
[8] Nesterov, Y. (2013) Introductory Lectures on Convex Optimization: A Basic Course (Vol. 87). Springer Science & Business Media, Berlin, Heidelberg.
[9] Bolte, J., Sabach, S. and Teboulle, M. (2014) Proximal Alternating Linearized Minimization for Nonconvex and Nonsmooth Problems. Mathematical Programming, 146, 459-494. [Google Scholar] [CrossRef] 
[10] Xu, Z., Chang, X., Xu, F. and Zhang, H. (2012) L1/2 Regularization: A Thresholding Representation Theory and a Fast Solver. IEEE Transactions on Neural Networks and Learning Systems, 23, 1013-1027. [Google Scholar] [CrossRef] 

为你推荐