Zhu, Yaochen On the convergence of sequential number-theoretic method for optimization. (English) Zbl 0995.65003 Acta Math. Appl. Sin., Engl. Ser. 17, No. 4, 532-538 (2001). 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. Reviewer: Ilya S.Molchanov (Glasgow) MSC: 65C05 Monte Carlo methods 11Z05 Miscellaneous applications of number theory 65K05 Numerical mathematical programming methods 90C30 Nonlinear programming Keywords:convergence; error bounds; sequential number-theoretic optimization method; algorithm; global maximum; quasi-Monte Carlo method PDF BibTeX XML Cite \textit{Y. Zhu}, Acta Math. Appl. Sin., Engl. Ser. 17, No. 4, 532--538 (2001; Zbl 0995.65003) Full Text: DOI References: [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) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.