非光滑约束优化基于非精确数据的改进水平束方法
A Modified Level Bundle Method with Inexact Data for Nonsmooth Constrained Optimization
DOI: 10.12677/AAM.2019.89179, PDF,    国家自然科学基金支持
作者: 李艳妮, 郑海艳, 唐春明：广西大学数学与信息科学学院，广西 南宁
关键词: 水平束方法；非精确数据；Bregman距离；全局收敛；复杂度分析；Level Bundle Method； Inexact Data； Bregman Distance； Global Convergence； Complexity Analysis
摘要: 本文提出了一个求解非光滑约束优化问题基于非精确数据的改进水平束方法。该方法引入了非精确数据及相应的近似改进函数。此外，通过在投影子问题中引入Bregman距离以代替传统的欧氏距离，从而可以充分利用可行集的几何集合，减少算法的计算量。最后证明了算法的全局收敛性并分析了迭代复杂度。
Abstract: This paper presents a modified level bundle method with inexact data for nonsmooth constrained optimization. In the method, the inexact data and the approximate improvement function are in-troduced. Moreover, in the projection subproblem, the Bregman distance is used to replace the classical Euclidean distance, in order that the geometric structure of the feasible set can be taken into account, which can reduce the computation of the algorithm. Global convergence of the algo-rithm is proved and the iterative complexity is analyzed.
文章引用：李艳妮, 郑海艳, 唐春明. 非光滑约束优化基于非精确数据的改进水平束方法[J]. 应用数学进展, 2019, 8(9): 1530-1538. https://doi.org/10.12677/AAM.2019.89179

参考文献

[1] Kiwiel, K.C. (1985) An Exact Penalty Function Algorithm for Non-Smooth Convex Constrained Minimization Prob-lems. IMA Journal of Numerical Analysis, 5, 111-119. [Google Scholar] [CrossRef] 
[2] Karas, E., Ribeiro, A., Sagastizábal, C., et al. (2009) A Bundle-Filter Method for Nonsmooth Convex Constrained Optimization. Mathematical Programming, 116, 297-320. [Google Scholar] [CrossRef] 
[3] Lemarechal, C., Nemirovskii, A. and Nesterov, Y. (1995) New Variants of Bundle Methods. Mathematical Programming, 69, 111-147. [Google Scholar] [CrossRef] 
[4] Fletcher, R. and Leyffer, S. (2002) Nonlinear Programming without a Penalty Function. Mathematical Programming, 91, 239-269. [Google Scholar] [CrossRef] 
[5] Van Ackooij, W. and De Oliveira, W. (2014) Level Bundle Methods for Constrained Convex Optimization with Various Oracles. Computational Optimization and Applications, 57, 555-597. [Google Scholar] [CrossRef] 
[6] Kiwiel, K.C. (1999) A Bundle Bregman Proximal Method for Convex Nondifferentiable Minimization. Mathematical Programming, 85, 241-258. [Google Scholar] [CrossRef] 
[7] Ben-Tal, A. and Nemirovski, A. (2005) Non-Euclidean Restricted Memory Level Method for Large-Scale Convex Optimization. Mathematical Programming, 102, 407-456. [Google Scholar] [CrossRef] 
[8] 梁玲. 非光滑优化基于非精确数据的加速水平束方法[D]: [硕士学位论文]. 南宁: 广西大学, 2018.
[9] 陈韵梅, 张维. 基于近似一阶信息的加速的bundle level算法[J]. 中国科学, 2017, 10(47): 1119-1142.

为你推荐