Boosters: A derivative-free algorithm based on radial basis functions

被引：34

作者：

Oeuvray, R. ^{[1
]}

Bierlaire, M. ^{[1
]}

机构：

[1] Transport and Mobility Laboratory, Ecolo Polytechnique, Fódóralc de Lausanne

来源：

International Journal of Modelling and Simulation | 2009年 / 29卷 / 01期

关键词：

Cuter; Dorivativo-froo optimization; Radial basis functions; Trust-region methods;

D O I：

10.2316/Journal.205.2009.1.205-4634

中图分类号：

学科分类号：

摘要：

Derivative-free optimization (DFO) involves the methods used to minimize an expensive objective function when its derivatives arc not available. Wo present hero a trust-region algorithm based on Radial Basis Functions (RBFs). The main originality of our approach is the use of RBFs to build the trust-region models and our management of the interpolation points based on Newton fundamental polynomials. Moreover the complexity of our method is very attractive. We have tested the algorithm against the best state-of-the-art methods (UOBYQA, NEWUOA, DFO). The tests on the problems from the CUTEr collection show that BOOSTERS is performing very well on medium-size problems. Moreover, it is able to solve problems of dimension 200, which is considered very largo in DFO.

引用

页码：26 / 36

页数：10

共 25 条

[1]

Lewis R.M., Torczon V., Trossot M.W., Direct search methods: Then and now, Journal of Computational and Applied Mathematics, 124, pp. 191-207, (2000)

[2]

Torczon V., On the convergence of pattern search algorithms, SIAM Journal on Optimization, 7, 1, pp. 1-25, (1997)

[3]

Neider J.A., Mead R., A simplex method for function minimization, Computer Journal, 7, pp. 308-313, (1965)

[4]

Rosonbrock H.H., An automatic method for finding the greatest or least value of a function, The Computer Journal, 3, pp. 175-184, (1960)

[5]

Powell M.J.D., An efficient method for finding the minimum of a function of several variables without calculating derivatives, Computer Journal, 17, pp. 155-162, (1964)

[6]

Conn A.R., Toint P.L., An algorithm using quadratic interpolation for unconstrained derivative free optimization, Nonlinear Optimization and Applications, pp. 27-47, (1996)

[7]

Powell M.J.D., UOBYQA: Unconstrained Optimization by Quadratic Approximation., (2000)

[8]

Powell M.J.D., The NEWUOA Software for Unconstrained Optimization Without Derivatives., (2004)

[9]

Booker A.J., Dennis J.E., Frank P.D., Sorafini D.B., Torczon V., Trossot M.W., A rigourous framework for optimization of expensive functions by surrogates, Structural Optimization, 17, 1, pp. 1-13, (1999)

[10]

Oouvray R., Trust-region Methods Based on Radial Basis Functions with Application to Biomedical Imaging, (2005)

← 1 2 3 →