A new Levenberg-Marquardt approach based on Conjugate gradient structure for solving absolute value equations

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rahpeymaii f.; AMINI K.; ALLAHVIRANLOO T.

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Journal: JOURNAL OF NEW RESEARCHES IN MATHEMATICS Year:2020 | Volume:5 | Issue:21 Page(s): 5-14

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Title

A new Levenberg-Marquardt approach based on Conjugate gradient structure for solving absolute value equations

Author(s)

rahpeymaii f. | AMINI K. | ALLAHVIRANLOO T. | Issue Writer Certificate

Keywords

Absolute value equationQ1

Levenberg-Marquardt approachQ1

Conjugate subgradient methodQ1

Global theoryQ1

Abstract

In this paper, we present a new approach for solving Absolute value equation (AVE) which use Levenberg-Marquardt method with conjugate subgradient structure. In Conjugate subgradient methods the new direction obtain by combining steepest descent direction and the previous di-rection which may not lead to good numerical results. Therefore, we replace the steepest descent direction by the Levenberg-Marquardt direction. The descent property of the direction generated by new algorithm in each iteration is established. Also, the global convergence of such a method are established under some mild assumptions. Some numerical results are reported. In this paper, we present a new approach for solving Absolute value equation (AVE) which use Levenberg-Marquardt method with conjugate subgradient structure. In Conjugate subgradient methods the new direction obtain by combining steepest descent direction and the previous di-rection which may not lead to good numerical results. Therefore, we replace the steepest descent direction by the Levenberg-Marquardt direction. The descent property of the direction generated by new algorithm in each iteration is established. Also, the global convergence of such a method are established under some mild assumptions. Some numerical results are reported.

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APA: Copy

rahpeymaii, f., AMINI, K., & ALLAHVIRANLOO, T.. (2020). A new Levenberg-Marquardt approach based on Conjugate gradient structure for solving absolute value equations. JOURNAL OF NEW RESEARCHES IN MATHEMATICS, 5(21 ), 5-14. SID. https://sid.ir/paper/257244/en

Vancouver: Copy

rahpeymaii f., AMINI K., ALLAHVIRANLOO T.. A new Levenberg-Marquardt approach based on Conjugate gradient structure for solving absolute value equations. JOURNAL OF NEW RESEARCHES IN MATHEMATICS[Internet]. 2020;5(21 ):5-14. Available from: https://sid.ir/paper/257244/en

IEEE: Copy

f. rahpeymaii, K. AMINI, and T. ALLAHVIRANLOO, “A new Levenberg-Marquardt approach based on Conjugate gradient structure for solving absolute value equations,” JOURNAL OF NEW RESEARCHES IN MATHEMATICS, vol. 5, no. 21 , pp. 5–14, 2020, [Online]. Available: https://sid.ir/paper/257244/en

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