A superlinearly convergent hybrid algorithm for systems of nonlinear equations
Department of Mathematics and Computer Science, Yangtze Normal University, Fuling, Chongqing, 408100, China
Journal of Inequalities and Applications 2012, 2012:180 doi:10.1186/1029-242X-2012-180Published: 24 August 2012
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.