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Modified mesh adaptive direct search algorithm withapproximate Hessian matrix(PDF)


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Modified mesh adaptive direct search algorithm withapproximate Hessian matrix
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
constrained optimization modified mesh adaptive direct search algorithm approximate Hessian matrix quadratic model funotions orthogonal triangular decomposition
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.


[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.


Last Update: 2018-04-30