A new Levenberg-Marquardt approach based on Conjugate gradient structure for solving absolute value equations
Subject Areas : Statistics
F.
Rahpeymaii
1
(Department of Mathematics, Science and research branch, Islamic Azad University, Tehran, Iran)
K.
Amini
2
(Razi university, Kermanshah, Iran)
T.
Allahviranloo
3
(Department of Mathematics, Science and research branch, Islamic Azad University, Tehran, Iran)
Keywords: معادله قدر مطلقی, روش لونبرگ-مارکوارت, همگرایی سراسری, روش گرادیان مزدوج,
Abstract :
In this paper, we present a new approach for solving absolute value equation (AVE) whichuse Levenberg-Marquardt method with conjugate subgradient structure. In conjugate subgradientmethods 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 descentdirection by the Levenberg-Marquardt direction. The descent property of the direction generatedby new algorithm in each iteration is established. Also, the global convergence of such a methodare established under some mild assumptions. Some numerical results are reported.In this paper, we present a new approach for solving absolute value equation (AVE) whichuse Levenberg-Marquardt method with conjugate subgradient structure. In conjugate subgradientmethods 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 descentdirection by the Levenberg-Marquardt direction. The descent property of the direction generatedby new algorithm in each iteration is established. Also, the global convergence of such a methodare established under some mild assumptions. Some numerical results are reported.
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