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AIMS Mathematics

2023, Volume 8, Issue 2: 4714-4725. doi: 10.3934/math.2023233
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Relaxed modified Newton-based iteration method for generalized absolute value equations

  • Department of Mathematics, College of Sciences, Northeastern University, Shenyang 110819, China
  • Received: 22 September 2022 Revised: 03 November 2022 Accepted: 18 November 2022 Published: 07 December 2022

  • MSC : 65F10, 90C05, 90C30

  • Many problems in different fields may lead to solutions of absolute value equations, such as linear programming problems, linear complementarity problems, quadratic programming, mixed integer programming, the bimatrix game and so on. In this paper, by introducing a nonnegative real parameter to the modified Newton-based iteration scheme, we present a new relaxed modified Newton-based (RMN) iteration method for solving generalized absolute value equations. The famous Picard iteration method and the modified Newton-type iteration method are the exceptional cases of the RMN iteration method. The convergence property of the new method is discussed. Finally, the validity and feasibility of the RMN iteration method are verified by experimental examples.

    Citation: Xin-Hui Shao, Wan-Chen Zhao. Relaxed modified Newton-based iteration method for generalized absolute value equations[J]. AIMS Mathematics, 2023, 8(2): 4714-4725. doi: 10.3934/math.2023233

    Related Papers:

  • Many problems in different fields may lead to solutions of absolute value equations, such as linear programming problems, linear complementarity problems, quadratic programming, mixed integer programming, the bimatrix game and so on. In this paper, by introducing a nonnegative real parameter to the modified Newton-based iteration scheme, we present a new relaxed modified Newton-based (RMN) iteration method for solving generalized absolute value equations. The famous Picard iteration method and the modified Newton-type iteration method are the exceptional cases of the RMN iteration method. The convergence property of the new method is discussed. Finally, the validity and feasibility of the RMN iteration method are verified by experimental examples.


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