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

Abstract

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