OALib Journal期刊
无约束优化的一个滤子非单调信赖域算法
DOI: 10.3969/j.issn.1001-8395.2015.02.014
Keywords: 无约束最优化 ,非单调信赖域算法 ,滤子 ,简单二次函数模型 ,收敛性
Abstract:
对无约束最优化问题提出了一个基于简单二次函数模型的非单调滤子信赖域算法.新算法中信赖域半径采用一个新的自适应调节策略.算法在每步迭代中以R-函数变化的速率和当前迭代点的信息来调节信赖域半径的大小,克服了传统信赖域算法中没有充分利用当前迭代点的信息调节信赖域半径的缺点.新算法在信赖域试探步不被接受时,采用滤子技术,增大试探步被接受的可能性;如果此试探步也不能被滤子集接受,则沿此试探步方向进行非单调线搜索得到步长.算法有别于传统的信赖域算法,没有重解子问题,减少了计算量.在较少的条件下,证明了算法的全局收敛性和超线性收敛性.
References
[1] Powell M J D. A new algorithm for unconstrained optimization[C]//Rosen J B, Mangassarian O L, Ritter K. Nonlinear Programming. New York:Academic Press,1970:31-66. [2] 孙清滢,段立宁,崔彬,等. 基于简单二次函数模型的非单调信赖域算法[J]. 系统科学与数学,2009,29(4):470-483. [3] 时贞军,孙国. 无约束优化问题的对角稀疏拟牛顿法[J]. 系统科学与数学,2006,26(1):101-112. [4] Fletcher R, Leyffer S. Nonlinear programming without a penalty function[J]. Math Program,2002,91:239-269. [5] Gould N I M, Sainvitu C, Toint Ph L. A filter-trust-region method for constrained optimization[J]. SIAM J Opt,2005,16:341-357. [6] Nocedal J, Yuan Y X. Combining Trust Region and Line Search Techniques[R]. Illinois:Northwestern University,1991. [7] Nocedal J, Yuan Y X. Combining trust region and line search techniques[J]. Advances in Nonlinear Programming,1998,14:153-175. [8] Sartenaer A. Automatic determination of an initial trust region in nonlinear programming[J]. SIAM J Sci Computing,1997,18:1788-1803. [9] Zhang X S, Zhang J L, Liao L Z. An adaptive trust region method and its convergence[J]. Science in China,2002,A45:620-631. [10] 李红,焦宝聪. 一类带线搜索的自适应信赖域算法[J]. 运筹学学报,2008,12(2):97-104. [11] Hei L. A self-adaptive trust region algorithm[J]. J Comput Math,2003,21:229-236. [12] Grippo L, Lamperiello F, Lucidi S. A nonmonotone line search technique for Newton’s method[J]. SIAM J Num Anal,1986,23:707-716. [13] Zhang H C, Hager William W. A nonmonotone line search technique and its application to unconstrained optimization[J]. SIAM J Opt,2004,14(4):1043-1056.
Full-Text
Contact Us
[email protected]
QQ:3279437679
WhatsApp +8615387084133
