Journal of Inequalities and Applications

, 2012:180

First online:

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A superlinearly convergent hybrid algorithm for systems of nonlinear equations

  • Lian ZhengAffiliated withDepartment of Mathematics and Computer Science, Yangtze Normal University Email author 


We propose a new algorithm for solving systems of nonlinear equations with convex constraints which combines elements of Newton, the proximal point, and the projection method. The convergence of the whole sequence is established under weaker conditions than the ones used in existing projection-type methods. We study the superlinear convergence rate of the new method if in addition a certain error bound condition holds. Preliminary numerical experiments show that our method is efficient.

MSC: 90C25, 90C30.


nonlinear equations projection method global convergence superlinear convergence