A superlinearly convergent projection method for constrained systems of nonlinear equations

Authors:
Chuanwei Wang;Yiju Wang
Affiliations:
College of Information Sciences and Engineering, Shandong Agricultural University, Tai'an, China 271018;School of Operations Research and Management Science, Qufu Normal University, Rizhao, China 276800
Venue:
Journal of Global Optimization
Year:
2009

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Abstract

In this paper, a new projection method for solving a system of nonlinear equations with convex constraints is presented. Compared with the existing projection method for solving the problem, the projection region in this new algorithm is modified which makes an optimal stepsize available at each iteration and hence guarantees that the next iterate is more closer to the solution set. Under mild conditions, we show that the method is globally convergent, and if an error bound assumption holds in addition, it is shown to be superlinearly convergent. Preliminary numerical experiments also show that this method is more efficient and promising than the existing projection method.