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http://hdl.handle.net/10397/93299
Title: | A generalized Newton method for a class of discrete-time linear complementarity systems | Authors: | Sun, Z Yang, X |
Issue Date: | 1-Oct-2020 | Source: | European journal of operational research, 1 Oct. 2020, v. 286, no. 1, p. 39-48 | Abstract: | In this paper, we propose a generalized Newton method for solving a class of discrete-time linear complementarity systems consisting of a system of linear equations and a linear complementarity constraints with a Z-matrix. We obtain a complete characterization of the least element solution of a linear complementarity problem with a Z-matrix that a solution is the least element solution if and only if the principal submatrix corresponding to the nonzero components of the solution is an M-matrix. We present a Newton method for solving a linear complementarity problem with a Z-matrix. We propose a generalized Newton method for solving the discrete-time linear complementarity system where the linear complementarity problem constraint is solved by the proposed Newton method. Under suitable conditions, we show that the generalized Newton method converges globally and finds a solution in finitely many iterations. Preliminary numerical results show the efficiency of the proposed method. | Keywords: | Finite termination Generalized Newton method Least element solution Linear complementarity system Linear rate of convergence Z-matrix |
Publisher: | Elsevier | Journal: | European journal of operational research | ISSN: | 0377-2217 | EISSN: | 1872-6860 | DOI: | 10.1016/j.ejor.2020.03.058 | Rights: | © 2020 Elsevier B.V. All rights reserved. © 2020. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/. The following publication Sun, Z., & Yang, X. (2020). A generalized Newton method for a class of discrete-time linear complementarity systems. European Journal of Operational Research, 286(1), 39-48 is available at https://dx.doi.org/10.1016/j.ejor.2020.03.058. |
Appears in Collections: | Journal/Magazine Article |
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