Bull. Korean Math. Soc. 2013; 50(3): 823-832
Printed May 31, 2013
https://doi.org/10.4134/BKMS.2013.50.3.823
Copyright © The Korean Mathematical Society.
Lian Zheng
Yangtze Normal University
We present a new algorithm for solving a system of nonlinear equations with convex constraints which combines proximal point and projection methodologies. Compared with the existing projection methods for solving the problem, we use a different system of linear equations to obtain the proximal point; and moreover, at the step of getting next iterate, our projection way and projection region are also different. Based on the Armijo-type line search procedure, a new hyperplane is introduced. Using the separate property of hyperplane, the new algorithm is proved to be globally convergent under much weaker assumptions than monotone or more generally pseudomonotone. We study the convergence rate of the iterative sequence under very mild error bound conditions.
Keywords: nonlinear equations, projection algorithm, global convergence, convergence rate
MSC numbers: 90C25, 90C33
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