On convergence of "divide the best" global optimization algorithms
In this paper a new class of multidimensional global optimization algorithms (called "divide the best" algorithms) is proposed. The class unifies and generalizes the classes of the characteristic methods and the adaptive partition algorithms introduced by Grishagin and Pinter respectively....
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| Published in: | Optimization Vol. 44; no. 3; pp. 303 - 325 |
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| Main Author: | |
| Format: | Journal Article |
| Language: | English |
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Gordon and Breach Science Publishers
01.01.1998
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| ISSN: | 0233-1934, 1029-4945 |
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| Abstract | In this paper a new class of multidimensional global optimization algorithms (called "divide the best" algorithms) is proposed. The class unifies and generalizes the classes of the characteristic methods and the adaptive partition algorithms introduced by Grishagin and Pinter respectively. The new scheme includes also some methods which do not fit either the characteristic or the adaptive partition families. A detailed convergence study is presented. A special attention is paid to cases where sufficient conditions of everywhere dense, local and global convergence are fulfilled only over subregions of the search domain. |
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| AbstractList | In this paper a new class of multidimensional global optimization algorithms (called "divide the best" algorithms) is proposed. The class unifies and generalizes the classes of the characteristic methods and the adaptive partition algorithms introduced by Grishagin and Pinter respectively. The new scheme includes also some methods which do not fit either the characteristic or the adaptive partition families. A detailed convergence study is presented. A special attention is paid to cases where sufficient conditions of everywhere dense, local and global convergence are fulfilled only over subregions of the search domain. |
| Author | Sergeyev, Yaroslav D. |
| Author_xml | – sequence: 1 givenname: Yaroslav D. surname: Sergeyev fullname: Sergeyev, Yaroslav D. organization: Nizhni Novgorod State University |
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| Cites_doi | 10.1016/0167-8191(92)90069-J 10.1007/BF01581266 10.1007/BF02238195 10.1016/0041-5553(72)90115-2 10.1007/BF01580583 10.1007/BF01876141 10.1007/BF01581202 10.1007/978-1-4757-2502-5 10.1007/3-540-50871-6 10.1007/BF02283683 10.1007/978-1-4615-2025-2 10.1007/BF01098365 10.1007/BF00939768 10.1007/BF01580907 10.1007/978-1-4757-2600-8_13 10.1016/0041-5553(89)90002-5 10.1007/BF00939434 10.1007/BF01096533 10.1007/978-3-662-03199-5 10.1023/A:1008242328176 |
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| References | Horst R. (CIT0016) 1995 Mladineo R. H. (CIT0022) 1986; 34 Baritompa W. (CIT0002) 1094; 4 Horst R. (CIT0018) 1988; 58 Strongin R. G. (CIT0035) 1978 Pinter J. (CIT0027) 1992; 56 Breiman L. (CIT0004) 1993; 58 Kushner H. A. (CIT0020) 1964; 86 Maclagan D. (CIT0021) Pinter J. (CIT0026) 1986; 36 Strongin R. G. (CIT0037) 1978 Horst R. (CIT0019) 1996 Hansen P. (CIT0015) 1992 Archetti F. (CIT0001) 1984; 1 Dixon L. C. W. (CIT0005) 1978; 2 Sergeyev Ya. D. (CIT0033) 1997 Fadeyev V. A. (CIT0006) Floudas C. A. (CIT0007) 1996 Pijavskii S. A. (CIT0024) 1972; 12 Sergeyev Ya. D. (CIT0031) 1994; 5 Gergel V. P. (CIT0008) 1992 Pinter J. (CIT0025) 1983 Strongin R. G. (CIT0036) 1992; 18 Sergeyev Ya. D. (CIT0034) 1990; 29 Horst R. (CIT0017) 1987; 54 Baritompa W. (CIT0003) 1991; 4 Grishagin V.A. (CIT0011); 1983 Hansen P. (CIT0014) 1995 Pardalos P. M. (CIT0023) 1990; 25 Grishagin V. A. . (CIT0010) 1979 Grishagin V.A. (CIT0012) 1991 Grishagin V. A. (CIT0013) 1997; 10 Gorodezkij S.Yu. (CIT0009) 1990 CIT0029 Strongin R. G. (CIT0038) 1992; 18 Torn A. (CIT0039) 1989 CIT0028 Rinnooy Kan A. H. G. (CIT0030) 1989 Sergeyev Ya. D. (CIT0032) 1995; 5 |
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| SubjectTerms | convergence Global optimization Mathematics Subject Classification 1991 numerical algorithms Primary: 90C30 Secondary: 49M37 |
| Title | On convergence of "divide the best" global optimization algorithms |
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