[1]刘 梅,刘红卫,杨善学,等.基于近似Hessian矩阵的修正网格自适应直接搜索算法[J].南京理工大学学报(自然科学版),2018,42(02):189.[doi:10.14177/j.cnki.32-1397n.2018.42.02.009]
 Liu Mei,Liu Hongwei,Yang Shanxue,et al.Modified mesh adaptive direct search algorithm withapproximate Hessian matrix[J].Journal of Nanjing University of Science and Technology,2018,42(02):189.[doi:10.14177/j.cnki.32-1397n.2018.42.02.009]
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基于近似Hessian矩阵的修正网格自适应直接搜索算法()
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《南京理工大学学报》(自然科学版)[ISSN:1005-9830/CN:32-1397/N]

卷:
42卷
期数:
2018年02期
页码:
189
栏目:
出版日期:
2018-04-30

文章信息/Info

Title:
Modified mesh adaptive direct search algorithm withapproximate Hessian matrix
文章编号:
1005-9830(2018)02-0189-06
作者:
刘 梅1刘红卫1杨善学2刘泽显13卢晓宁1
1.西安电子科技大学 数学与统计学院,陕西 西安 710126; 2.西安财经学院 统计学院,陕西 西安 710100; 3.贺州学院 数学与计算机学院,广西 贺州 542899
Author(s):
Liu Mei1Liu Hongwei1Yang Shanxue2Liu Zexian13Lu Xiaoning1
1.School of Mathematics and Statistic,Xidian University,Xi’an 710126,China; 2.School of Statistics,Xi’an University of Finance and Economics,Xi’an 710100,China; 3.School of Mathematics and Computer Science,Hezhou University,Hezhou 542899,China
关键词:
约束优化 修正网格自适应直接搜索算法 近似Hessian矩阵 二次模型函数 正交三角分解
Keywords:
constrained optimization modified mesh adaptive direct search algorithm approximate Hessian matrix quadratic model funotions orthogonal triangular decomposition
分类号:
O221.2
DOI:
10.14177/j.cnki.32-1397n.2018.42.02.009
摘要:
针对网格自适应直接搜索算法寻优效率低和收敛速度慢的问题,提出了一种基于近似Hessian矩阵的修正网格自适应直接搜索算法。基于正交三角分解,提出一种产生探测方向集的算法,用于构建搜索步目标函数的二次模型函数和约束函数的线性模型函数。运用泰勒展开式、秩一校正及线性回归的思想,并改变部分参数解决子问题,得到局部最优解。在探测步中,以试验点为中心按照新的探测方向集进行局部搜索,在理论上证明了新算法的收敛性。通过对不同维数的测试函数分析可知,与原始的网格自适应直接搜索算法相比,该算法的迭代次数明显减少。
Abstract:
In order to solve the problem that the mesh adaptive direct search algorithm is easily failing into slow convergence and low efficiency when optimizing,the modified mesh adaptive direct search algorithm with the second directional derivative-based Hessian matrix is presented. The orthogonal triangular decomposition is applied to the presented algorithm. In search step,using the Taylor series expansion,the rank-one update and the linear regression,the quadratic model of the function with linear constrains is built by means of a second directional derivative-based Hessian matrix. By solving the subprogram of the problem,the local solution is obtained. The poll step searchs the best point according to the new poll directions in the neighbor of the trial points,and the update of the poll directions and some parameters is altered in this method. The modified algorithm outperforms the original algorithm in terms of iteration times on some test problems.

参考文献/References:

[1] 蔡志杰,陈德强. 非线性优化的直接搜索算法及收敛性证明[J]. 复旦学报(自然科学版),2006,45(3):396-403.
Cai Zhijie,Chen Deqiang. Direct search algorithm for nonlinear optimization and convergence analysis[J]. Journal of Fudan University(Natural Science),2006,45(3):396-403.
[2]黄天云. 约束优化模式搜索法研究进展[J]. 计算机学报,2008,31(7):1200-1215.
Huang Tianyun. Research advances on pattern searches in constrained optimization[J]. Journal of Computers,2008,31(7):1200-1215.
[3]Audet C,Dennis J E. Mesh adaptive direct search algorithms for constrained optimization[J]. SIAM Jounal on Optimization,2006,17(1):188-217.
[4]Custódio A L,Rocha H,Vincente L N. Incorporating minimum Frobenius norm models in direct search[J]. Computation Optimization Application,2010,46(2):265-278.
[5]Powell M J D. Development of NEWUOA for minimization without derivatives[J]. IMA Jounal of Numerical Analysis,2008,28:649-664.
[6]Conn A R,Le Digabel S. Use of quadratic models with mesh-adaptive direct search for constrained black box optimization[J]. Optimization Methods & Software,2013,28(1):139-158.
[7]Burmen A,Olensek J,Tuma T. Mesh adaptive direct search with second directional derivative-based Hessian matrix[J]. Computation Optimization Application,2015,62:693-715.
[8]Audet C,Custódio A L,Dennis J E. Erratum:mesh adaptive direct search algorithms for constrained optimization[J]. SIAM Jounal Optimization,2007,18(4):1501-1503.
[9]Abramson M A,Audet C,Dennis J E,et al. Ortho MADS:a deterministic MADS instance with orthogonal directions[J]. SIAM Journal on Optimization,2009,20(2):948-966.
[10]Van Dyke B,Asaki T J. Using QR decomposition to obtain a new instance of mesh adaptive direct search with uniformly distributed polling directions[J]. Jounal Optimization Theory Application,2013,159(3):805-821.
[11]Leventhal D,Lewis A S. Randomized Hessian estimation and directional search[J]. Optimization,2011,60(3):329-345.
[12]Conn A R,Scheinberg K,Vicente L N. Introduction to derivative-free optimization[M]. Philadelphia,US:Socoety for Industrial and Applied Mathematics,2009:15-23.
[13]王娟娟. 一般约束的网格自适应直接搜索过滤算法[D]. 南京:南京理工大学理学院,2012.
[14]Karmitsa N. Test problems for large-scale nonsmooth minimization[R]. Jyv?skvl?,Finland:University of Jyv?skvl?,2007.
[15]Hock W,Schittkowski K. Test examples for nonlinear programming codes[J]. Lecture Notes in Economics and Mathematical Systems,1981,187:1-177.

备注/Memo

备注/Memo:
收稿日期:2017-06-06 修回日期:2017-08-29
基金项目:国家自然科学基金(11461021); 广西高校科研项目(2013YB236)
作者简介:刘梅(1992-),女,硕士生,主要研究方向:无导数优化算法及应用,E-mail:meiliuxidian @163.com; 通讯作者:刘泽显(1984-),男,博士生,讲师,主要研究方向:最优化理论与方法,E-mail:liuzexian2008@163.com。
引文格式:刘梅,刘红卫,杨善学,等. 基于近似Hessian矩阵的修正网格自适应直接搜索算法[J]. 南京理工大学学报,2018,42(2):189-194.
投稿网址:http://zrxuebao.njust.edu.cn
更新日期/Last Update: 2018-04-30