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On the convergence of sequential number-theoretic method for optimization. (English) Zbl 0995.65003
The author investigates convergence properties and error bounds for the sequential number-theoretic optimization method proposed by K. T. Fang, Y. Wang and K.-T. Huan [Number-theoretic method in statistics (Chapman & Hall, London) (1994; Zbl 0925.65263)]. This method is applied to formulate an algorithm to find a global maximum of a multivariate function, where it is more efficient in some cases than the standard quasi-Monte Carlo method.
MSC:
65C05 Monte Carlo methods
11Z05 Miscellaneous applications of number theory
65K05 Numerical mathematical programming methods
90C30 Nonlinear programming
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[1] H. Niederreiter, K. McCurley. Optimization of Functions by Quasi-random Search Methods.Computing, 1979, 22(2): 119–123 · Zbl 0405.65042 · doi:10.1007/BF02253124
[2] H. Niederreiter. A Quasi-Monte Carlo Method for the Approximate Computation of the Extreme Values of a Function. Studies in Pure Math., Birkhäuser, Basel, 1983, 523–529 · Zbl 0527.65041
[3] K.-T. Fang, Y. Wang. A Sequential Algorithm for Optimization and Its Application to Regression Analysis. Technical Report, Inst. of Appl. Math., Academia Sinica, Beijing, 1989
[4] K.-T. Fang Y. Wang. Number-theoretic Methods in Statistics. Chapman & Hall, London, 1994 · Zbl 0925.65263
[5] H. Niederreiter. Random Number Generation and Quasi-Monte Carlo Methods. SIAM, Philadelphia, 1992. · Zbl 0761.65002
[6] I.M. Sobol. On Functions Satisfying a Lipschitz Condition in Multidimensional Problems of Computitational Mathematics.Dokl. Akad. Nauk SSSR, 1987, 293(6): 1314–1319 (in Russian)
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