A derivative-free filter method for solving nonlinear complementarity problems
In this work, nonlinear complementarity problems (NCPs) are considered. Some NCPs, which come from practice, have no derivatives or it is very difficult to obtain their derivatives. Derivative-free methods are hence considered. Generalized pattern search (GPS) method, as a kind of derivative-free me...
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| Vydané v: | Applied mathematics and computation Ročník 161; číslo 3; s. 787 - 797 |
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| Hlavní autori: | , |
| Médium: | Journal Article |
| Jazyk: | English |
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New York, NY
Elsevier Inc
2005
Elsevier |
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| ISSN: | 0096-3003, 1873-5649 |
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| Abstract | In this work, nonlinear complementarity problems (NCPs) are considered. Some NCPs, which come from practice, have no derivatives or it is very difficult to obtain their derivatives. Derivative-free methods are hence considered. Generalized pattern search (GPS) method, as a kind of derivative-free method, plays a very significant role. We combine generalized pattern search method with filter method to attack NCPs because one can analyze the theory of generalized pattern search filter method without sufficient reduction conditions and avoid using of derivatives. Some interesting results are obtained in this work without sufficient reduction conditions. Furthermore, generalized pattern search filter method is efficient to some special problems. |
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| AbstractList | In this work, nonlinear complementarity problems (NCPs) are considered. Some NCPs, which come from practice, have no derivatives or it is very difficult to obtain their derivatives. Derivative-free methods are hence considered. Generalized pattern search (GPS) method, as a kind of derivative-free method, plays a very significant role. We combine generalized pattern search method with filter method to attack NCPs because one can analyze the theory of generalized pattern search filter method without sufficient reduction conditions and avoid using of derivatives. Some interesting results are obtained in this work without sufficient reduction conditions. Furthermore, generalized pattern search filter method is efficient to some special problems. |
| Author | Fan, Jin-yan Nie, Pu-yan |
| Author_xml | – sequence: 1 givenname: Pu-yan surname: Nie fullname: Nie, Pu-yan email: conver001@yahoo.com.cn organization: Department of Mathematics, College of Information Science and Technology, Jinan University, Guangzhou 510632, PR China – sequence: 2 givenname: Jin-yan surname: Fan fullname: Fan, Jin-yan organization: Department of Mathematics, Shanghai Jiaotong University, Shanghai 200240, PR China |
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| Cites_doi | 10.1016/S0096-3003(03)00135-8 10.1007/BF01586928 10.1080/10556789408805573 10.1137/S1052623493250780 10.1007/s002110050133 10.1007/BF00249054 10.1007/BF02614396 10.1007/s101070100244 10.1137/S105262340038081X |
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| Keywords | Filter methods Global convergence Nonlinear complementarity problem Nonlinear programming Generalized pattern search methods Reduction method Sufficient condition Applied mathematics Complementarity problem Nonlinear problems Non linear programming Pattern recognition Convergence Filter method |
| Language | English |
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| References | Torczon (BIB12) 1997; 7 Fischer (BIB3) 1997; 76 Fletcher, Leyffer (BIB4) 2002; 91 Kanzow (BIB7) 1994; 3 Cottle, Pang, Stone (BIB2) 1992 Pang (BIB10) 1991; 51 Fletcher, Leyffer, Toint (BIB5) 2002; 13 Nie (BIB8) 2003; 21 C. Audet, J.E. Dennis, Jr., Combining patter search and filter algorithms for derivative free optimization, TR00-9 Department of Computational and Applied Mathematics, Rice University, Houston, TX, 2000 Yuan (BIB11) 1995; 70 Geiger, Kanzow (BIB6) 1996; 5 Nie (BIB9) 2004; 149 Fletcher (10.1016/j.amc.2003.12.038_BIB4) 2002; 91 Yuan (10.1016/j.amc.2003.12.038_BIB11) 1995; 70 Nie (10.1016/j.amc.2003.12.038_BIB9) 2004; 149 Fischer (10.1016/j.amc.2003.12.038_BIB3) 1997; 76 Torczon (10.1016/j.amc.2003.12.038_BIB12) 1997; 7 Geiger (10.1016/j.amc.2003.12.038_BIB6) 1996; 5 Fletcher (10.1016/j.amc.2003.12.038_BIB5) 2002; 13 Pang (10.1016/j.amc.2003.12.038_BIB10) 1991; 51 Cottle (10.1016/j.amc.2003.12.038_BIB2) 1992 Nie (10.1016/j.amc.2003.12.038_BIB8) 2003; 21 10.1016/j.amc.2003.12.038_BIB1 Kanzow (10.1016/j.amc.2003.12.038_BIB7) 1994; 3 |
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| SubjectTerms | Applied sciences Artificial intelligence Calculus of variations and optimal control Computer science; control theory; systems Exact sciences and technology Filter methods Generalized pattern search methods Global convergence Mathematical analysis Mathematical programming Mathematics Nonlinear complementarity problem Nonlinear programming Operational research and scientific management Operational research. Management science Pattern recognition. Digital image processing. Computational geometry Sciences and techniques of general use |
| Title | A derivative-free filter method for solving nonlinear complementarity problems |
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