zbMATH — the first resource for mathematics

A cut-peak function method for global optimization. (English) Zbl 1166.65030
Summary: A new method is proposed for solving box constrained global optimization problems. The basic idea of the method is described as follows: Constructing a so-called cut-peak function and a choice function for each present minimizer, the original problem of finding a global solution is converted into an auxiliary minimization problem of finding local minimizers of the choice function, whose objective function values are smaller than the previous ones. For a local minimum solution of auxiliary problems this procedure is repeated until no new minimizer with a smaller objective function value could be found for the last minimizer. Construction of auxiliary problems and choice of parameters are relatively simple, so the algorithm is relatively easy to implement, and the results of the numerical tests are satisfactory compared to other methods.

65K05 Numerical mathematical programming methods
90C30 Nonlinear programming
90C59 Approximation methods and heuristics in mathematical programming
Full Text: DOI
[1] Ge., R., The globally convexized filled functions for global optimization, Appl. math. comput., 35, 131-158, (1990) · Zbl 0752.65052
[2] Ge., R.P.; Qin, Y.F., A class of filled functions for finding global minimizers of a function of several variables, J. optim. theory appl., 54, 2, 241-252, (1987) · Zbl 0595.65072
[3] Liang, Y.M.; Zhang, L.S.; Li., M.M.; Han, B.S., A filled function method for global optimization, J. comput. appl. math., 205, 1, 16-31, (2007) · Zbl 1124.65052
[4] Liu, X.; Xu., W., A new filled function applied to global optimization, Comput. oper. res., 31, 61-80, (2004) · Zbl 1039.90099
[5] Levy, A.V.; Montalvo, A., The tunneling algorithm for the global minimization of functions, SIAM J. sci. stat. comput., 6, 1, 15-29, (1985) · Zbl 0601.65050
[6] Yao, Y., Dynamic tunneling algorithm for global optimization, IEEE trans. systems man cybernet., 19, 5, 1222-1230, (1989)
[7] Gómezy, S.; Levy, A.V., The tunneling method for solving the constrained global optimization problem with several non-connected feasible regions, (), 34-47
[8] Polak, E.; Royset, J.O.; Womersley, R.S., Algorithms with adaptive smoothing for finite minimax problems, J. optim. theory appl., 119, 3, 459-484, (2003) · Zbl 1061.90117
[9] Broyden, C.G., The convergence of a class of double-rank minimization algorithms, J. inst. math. appl., 6, 76-90, (1970) · Zbl 0223.65023
[10] Fletcher, R., A new approach to variable metric algorithms, Comput. J., 13, 317-322, (1970) · Zbl 0207.17402
[11] Goldfarb, D., A family of variable metric updates derived by variational means, Math. comput., 24, 23-26, (1970) · Zbl 0196.18002
[12] Shanno, D.F., Conditioning of quasi-Newton methods for function minimization, Math. comput., 24, 647-656, (1970) · Zbl 0225.65073
[13] Armijo, L., Minimization of functions having Lipschitz-continuous first partial derivatives, Pacific J. math., 16, 1-3, (1966) · Zbl 0202.46105
[14] Branin, F., Wildly convergent methods for finding multiple solutions of simultaneous nonlinear equations, IBM J. res. dev., 16, 5, 504-522, (1972) · Zbl 0271.65034
[15] Branin, F.; Hoo, S., A method for finding multiple extrema of a function of n variables, () · Zbl 0271.65035
[16] ()
[17] C. Barróny, S. Gómez, The exponential tunneling method, Reporte de Investigación IIMAS, vol. 1 No. 3, 1991
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.