A new projection algorithm for solving\break a system of nonlinear equations\break with convex constraints
Bull. Korean Math. Soc. 2013 Vol. 50, No. 3, 823-832
Printed May 31, 2013
Lian Zheng
Yangtze Normal University
Abstract : 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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