A derivative-free memoryless BFGS hyperplane projection method for solving large-scale nonlinear monotone equations
In this work, by combining a three-term memoryless BFGS conjugate gradient direction with the hyperplane projection technique , we develop a new derivative-free algorithm to solve nonlinear monotone equations. The method is motivated by conjugate gradient method and hyperplane projection, as well as...
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| Veröffentlicht in: | Soft computing (Berlin, Germany) Jg. 27; H. 7; S. 3805 - 3815 |
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01.04.2023
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| Abstract | In this work, by combining a three-term memoryless BFGS conjugate gradient direction with the hyperplane projection technique , we develop a new derivative-free algorithm to solve nonlinear monotone equations. The method is motivated by conjugate gradient method and hyperplane projection, as well as quasi-Newton method. The search direction has three terms and is obtained by modifying the BFGS updating matrix with a unit matrix in each step. The algorithm needs no matrices computing, and it is suitable for solving large-scale nonlinear monotone equations. The proposed method satisfies the Dai–Liao conjugacy conditions and is always descent irrelative to any line searches. Under standard conditions, the optimizer solution can be obtained by a globally convergent sequence as long as the initial point is given. The reported numerical experiments show that the method is promising and efficient compared to similar algorithms in the literature. |
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| AbstractList | In this work, by combining a three-term memoryless BFGS conjugate gradient direction with the hyperplane projection technique , we develop a new derivative-free algorithm to solve nonlinear monotone equations. The method is motivated by conjugate gradient method and hyperplane projection, as well as quasi-Newton method. The search direction has three terms and is obtained by modifying the BFGS updating matrix with a unit matrix in each step. The algorithm needs no matrices computing, and it is suitable for solving large-scale nonlinear monotone equations. The proposed method satisfies the Dai–Liao conjugacy conditions and is always descent irrelative to any line searches. Under standard conditions, the optimizer solution can be obtained by a globally convergent sequence as long as the initial point is given. The reported numerical experiments show that the method is promising and efficient compared to similar algorithms in the literature. |
| Author | Huang, Fei Deng, Songhai Tang, Jinyuan |
| Author_xml | – sequence: 1 givenname: Fei surname: Huang fullname: Huang, Fei organization: School of Mathematics and Statistics, Central South University – sequence: 2 givenname: Songhai orcidid: 0000-0002-5074-4791 surname: Deng fullname: Deng, Songhai email: dsonghai@163.com organization: School of Mathematics and Statistics, Central South University – sequence: 3 givenname: Jinyuan surname: Tang fullname: Tang, Jinyuan organization: State Key Lab High Performance Complex Mfg, Central South University |
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| Cites_doi | 10.1007/s12652-020-02270-x 10.1080/10556780310001610493 10.1109/ACCESS.2020.2992340 10.1007/s40031-019-00398-9 10.1007/s10470-019-01556-1 10.1016/j.camwa.2015.09.014 10.3390/math8020168 10.1007/s11075-019-00658-1 10.1016/j.cam.2012.10.002 10.1093/imanum/drl016 10.1007/s12652-020-02746-w 10.1007/s002450010019 10.1093/imanum/drq015 10.1007/s101070100263 10.1007/s00211-006-0028-z 10.1007/s11075-012-9653-z 10.1080/10556788.2013.833199 10.1007/s11075-018-0541-z 10.1007/s10288-016-0323-1 10.1007/s11042-018-6109-z 10.1007/s11277-021-08411-5 10.1016/j.ejor.2009.11.030 10.1007/s11220-020-0272-9 10.1007/s11075-018-0479-1 10.1016/j.jmaa.2013.04.017 10.1007/b98874 10.1007/978-1-4757-6388-1_18 10.1016/j.cam.2010.01.001 |
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| Keywords | Conjugate gradient method Nonlinear monotone equations Derivative-free method Hyperplane projection method |
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