A superlinearly convergent ODE-type trust region algorithm for nonsmooth nonlinear equations
This paper presents a new trust region algorithm for solving nonsmooth nonlinear equation problems which posses the smooth plus non-smooth decomposition. At each iteration, this method obtains a trial step by solving a system of linear equations, hence avoiding the need for solving a quadratic progr...
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| Vydané v: | Journal of applied mathematics & computing Ročník 22; číslo 3; s. 371 - 380 |
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| Médium: | Journal Article |
| Jazyk: | English |
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Dordrecht
Springer Nature B.V
01.10.2006
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| ISSN: | 1598-5865, 1865-2085 |
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| Abstract | This paper presents a new trust region algorithm for solving nonsmooth nonlinear equation problems which posses the smooth plus non-smooth decomposition. At each iteration, this method obtains a trial step by solving a system of linear equations, hence avoiding the need for solving a quadratic programming subproblem with a trust region bound. From a computational point of view, this approach may reduce computational effort and hence improve computational efficiency. Furthermore, it is proved under appropriate assumptions that this algorithm is globally and locally super-linearly convergent. Some numerical examples are reported.[PUBLICATION ABSTRACT] |
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| AbstractList | This paper presents a new trust region algorithm for solving nonsmooth nonlinear equation problems which posses the smooth plus non-smooth decomposition. At each iteration, this method obtains a trial step by solving a system of linear equations, hence avoiding the need for solving a quadratic programming subproblem with a trust region bound. From a computational point of view, this approach may reduce computational effort and hence improve computational efficiency. Furthermore, it is proved under appropriate assumptions that this algorithm is globally and locally super-linearly convergent. Some numerical examples are reported. This paper presents a new trust region algorithm for solving nonsmooth nonlinear equation problems which posses the smooth plus non-smooth decomposition. At each iteration, this method obtains a trial step by solving a system of linear equations, hence avoiding the need for solving a quadratic programming subproblem with a trust region bound. From a computational point of view, this approach may reduce computational effort and hence improve computational efficiency. Furthermore, it is proved under appropriate assumptions that this algorithm is globally and locally super-linearly convergent. Some numerical examples are reported.[PUBLICATION ABSTRACT] |
| Author | Yigui, Ou |
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| CitedBy_id | crossref_primary_10_1007_s12190_008_0132_6 crossref_primary_10_1007_s11590_020_01558_3 crossref_primary_10_1016_j_cam_2009_06_012 crossref_primary_10_1080_01630563_2011_563157 crossref_primary_10_1016_j_amc_2014_01_171 |
| Cites_doi | 10.1007/BF01582255 10.1287/moor.17.3.586 10.1137/0805011 10.1007/BF01581275 10.1007/BF01582577 |
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| Copyright | Korean Society for Computational & Applied Mathematics and Korean SIGCAM 2006 |
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| DOI | 10.1007/BF02832062 |
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| References | Ke Xiaowu (BF02832062_CR9) 1998; 34 Y. Yuan (BF02832062_CR1) 1997 L. Qi (BF02832062_CR4) 1993; 58 L. Qi (BF02832062_CR8) 1994; 64 A. A. Brown (BF02832062_CR7) 1989; 62 BF02832062_CR11 M. J. D. Powell (BF02832062_CR10) 1970 S. P. Han (BF02832062_CR3) 1992; 17 P. T. Harker (BF02832062_CR2) 1990; 48 L. Qi (BF02832062_CR5) 1995; 5 W. Sun (BF02832062_CR6) 1999; 105 |
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| Title | A superlinearly convergent ODE-type trust region algorithm for nonsmooth nonlinear equations |
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