Yue, Lina; Yang, Yongjian A new integral filter algorithm for unconstrained global optimization. (English) Zbl 1272.65055 Numer. Algorithms 63, No. 3, 419-430 (2013). This paper proposes an exponential integral filter algorithm in solving unconstrained global optimization problems. A quasi-Newton method search is used for the local minimum, and the Monte Carlo method is used for integral operation. The convergence of the algorithm is established under certain mild condition. Some numerical results in solving five test problems are presented. Reviewer: Hang Lau (Montréal) Cited in 2 Documents MSC: 65K05 Numerical mathematical programming methods 90C26 Nonconvex programming, global optimization 90C53 Methods of quasi-Newton type 65C05 Monte Carlo methods 90C57 Polyhedral combinatorics, branch-and-bound, branch-and-cut Keywords:global optimization; integral filter; branch and bound; local search algorithm; quasi-Newton method; Monte Carlo method; convergence; numerical results PDFBibTeX XMLCite \textit{L. Yue} and \textit{Y. Yang}, Numer. Algorithms 63, No. 3, 419--430 (2013; Zbl 1272.65055) Full Text: DOI References: [1] Yang, Y.J., Du, X.W., Li, M.M.: A integral filter algorithm for unconstrained global optimization. Appl. Math. Comput. 18, 173-180 (2007) · Zbl 1116.65075 · doi:10.1016/j.amc.2006.05.147 [2] Pardalos, P., Romejin, H.E.: Handbook of Global Optimization, vol. 2. Kluwer Academic Publishers (2002) · Zbl 0694.90083 [3] Zhigljavsky, A., Zilinskas, A.: Stochastic Global Optimization. Springer, New York (2008) · Zbl 1136.90003 [4] Storgin, R.G., Sergeyev, Y.D.: Global Optimization with Non-convex Constraints. Springer, New York (2000) · Zbl 0601.65050 [5] Levy, A.B.: The tunneling algorithm for the global minimization of function. SIAM J. Sci. Stat. Comput. 6, 15-29 (1985) · Zbl 0601.65050 · doi:10.1137/0906002 [6] Ge, R.P.: A filled function method for finding a global minimizer of a function of several variables. Math. Program. 46, 191-204 (1990) · Zbl 0694.90083 · doi:10.1007/BF01585737 [7] Horst, R., Pardalos, P.M., Thoai, N.V.: Introduction to Global Optimization. Kluwer Academic Publishers (1995) · Zbl 0836.90134 [8] Liu, H.L., Ye, F.: Realization of Monte Carlo method by using uniform random sequence for calculating multiple integrals, (in Chinese). Computer Knowledge and Technology 4(35), 2289-2291 (2008) 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.