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Global descent method for constrained continuous global optimization. (English) Zbl 1335.90073
Summary: In this paper, we consider the problem of constrained global optimization of a continuous multivariable function. We propose a global descent function technique which requires an easily adjustable single parameter. The characteristic property of the proposed function is that each of its local minimizers verifying constraints is a better local minimizer of the objective function, or at less, an approximated local minimizer with a given tolerance. Several other properties of the new function are investigated, in order to establish a corresponding optimization algorithm. We have performed numerical experiments on a set of standard test problems using this algorithm; the results illustrate the efficiency of our approach.

90C26 Nonconvex programming, global optimization
90C56 Derivative-free methods and methods using generalized derivatives
Full Text: DOI
[1] Ge, R. P., A filled function for finding global minimizer of a function of several variables, Math. Program., 46, 191-204, (1990) · Zbl 0694.90083
[2] Ge, R. P.; Qin, Y., The globally convexized filled functions for global optimization, Appl. Math. Comput., 35, 2, 131-158, (1990) · Zbl 0752.65052
[3] Rahal, M.; Ziadi, A., A new extension of piyavskii’s method to Hölder functions of several variables, Appl. Math. Comput., 197, 478-488, (2008) · Zbl 1154.65050
[4] Vanderbei, R. J., Extension of piyavskii’s algorithm to continuous global optimization, J. Global Optim., 14, 205-216, (1999) · Zbl 0946.90065
[5] He, S.; Chen, W.; Wang, H., A new filled function algorithm for constrained global optimization problems, Appl. Math. Comput., 217, 5853-5859, (2011) · Zbl 1210.65110
[6] Lin, H.; Wang, Y.; Fan, L., A filled function method with one parameter for unconstrained global optimization, Appl. Math. Comput., 218, 3776-3785, (2011) · Zbl 1244.65083
[7] Ng, C.-K.; Li, D.; Zhang, L.-S., Global descent method for global optimization, SIAM J. Optim., 20, 6, 3161-3184, (2010) · Zbl 1208.49038
[8] Wu, Z. Y.; Li, D.; Zhang, L. S., Global descent methods for unconstrained global optimization, J. Global Optim., 50, 3, 379-396, (2011) · Zbl 1228.90089
[9] Wu, Z. Y.; Bai, F. S.; Yang, Y. J.; Mammadova, M., A new auxiliary function method for general constrained, Optimization, 62, 2, 193-210, (2013) · Zbl 1291.90193
[10] Liu, X., The impelling function method applied to global optimization, Appl. Math. Comput., 151, 745-754, (2004) · Zbl 1055.65077
[11] Goldberg, D., Genetic algorithms in search, optimization and machine learning, (1989), Addison-Wesley · Zbl 0721.68056
[12] Kirkpatrick, S.; Gelatt, D.; Vecchi, M. P., Optimization by simulate annealing, Science, 220, 671-680, (1983) · Zbl 1225.90162
[13] Ali, M. M.; Torn, A.; Viitanen, S., A numerical comparison of some modified controlled random search algorithms, J. Global Optim., 11, 377-385, (1997) · Zbl 0891.90144
[14] Storn, R.; Price, K., Differential evolution - a simple and efficient heuristic for global optimization over continuous spaces, J. Global Optim., 11, 341-359, (1997) · Zbl 0888.90135
[15] Yang, Y. J.; Shang, Y. L., A new filled function method for unconstrained global optimization, Appl. Math. Comput., 173, 501-512, (2006) · Zbl 1094.65063
[16] Horst, R.; Tuy, H., Global optimization, Deterministic Approach, (1993), Springer-Verlag Berlin
[17] Tuy, H., Convex analysis and global optimization, (1998), Kluwer Academic Publishers Dordrecht · Zbl 0904.90156
[18] Xu, Z.; Huang, H. X.; Pardalos, P., Filled functions for unconstrained global optimization, J. Global Optim., 20, 49-65, (2001) · Zbl 1049.90092
[19] Zhang, Y.; Xu, Y. T.; Zhang, L. S., A filled function method applied to nonsmooth constrained global optimization, J. Comput. Appl. Math., 232, 415-426, (2009) · Zbl 1175.90422
[20] Zhang, Y.; Xu, Y. T., A one-parameter filled function method applied to nonsmooth constrained global optimization, Comput. Math. Appl., 58, 1230-1238, (2009) · Zbl 1189.90128
[21] Horst, R.; Pardalos, P. M.; Thoai, N. V., Introduction to global optimization, (2000), Kluwer Academic Publishers Dordrecht · Zbl 0966.90073
[22] Hansen, E., Global optimization using interval analysis, (1992), Marcel Dekker New York · Zbl 0762.90069
[23] Levy, A. V.; Montalvo, A. M., The tunneling algorithm for the global minimization of functions, SIAM J. Sci. Stat. Comput., 6, 1, 15-29, (1985) · Zbl 0601.65050
[24] Yao, Y., Dynamic tunneling algorithm for global optimization, IEEE Trans. Syst. Man Cybern., 19, 5, 1222-1230, (1989)
[25] Zhu, W.; Fu, Q., A sequential convexification method (SCM) for continuous global optimization, J. Global Optim., 26, 167-182, (2003) · Zbl 1049.90069
[26] Robertson, B. L.; Price, C. J.; Reale, M., Cartopt: a random search method for nonsmooth unconstrained optimization, Comput. Optim. Appl., 56, 2, 291-315, (2013) · Zbl 1312.90065
[27] B.L. Robertson, Direct search methods for nonsmooth problems using global optimization techniques. (Ph.D. thesis), University of Canterbury, Christchurch, New Zealand, 2010.
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