Partitioned quasi-Newton methods for sparse nonlinear equations

Hui-Ping Cao () and Dong-Hui Li ()
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Hui-Ping Cao: Hunan University
Dong-Hui Li: South China Normal University

Computational Optimization and Applications, 2017, vol. 66, issue 3, No 4, 505 pages

Abstract: Abstract In this paper, we present two partitioned quasi-Newton methods for solving partially separable nonlinear equations. When the Jacobian is not available, we propose a partitioned Broyden’s rank one method and show that the full step partitioned Broyden’s rank one method is locally and superlinearly convergent. By using a well-defined derivative-free line search, we globalize the method and establish its global and superlinear convergence. In the case where the Jacobian is available, we propose a partitioned adjoint Broyden method and show its global and superlinear convergence. We also present some preliminary numerical results. The results show that the two partitioned quasi-Newton methods are effective and competitive for solving large-scale partially separable nonlinear equations.

Keywords: Partially separable nonlinear equation; Partitioned Broyden’s rank one method; Partitioned adjoint Broyden method; Global convergence; Superlinear convergence; 65K05; 90C06; 90C53 (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s10589-016-9878-1

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