Spectral gradient projection method for monotone nonlinear equations with convex constraints

Authors:
Zhensheng Yu;Ji Lin;Jing Sun;Yunhai Xiao;Liying Liu;Zhanhui Li
Affiliations:
College of Science, University of Shanghai for Science and Technology, Shanghai, 200093, China;College of Science, University of Shanghai for Science and Technology, Shanghai, 200093, China;College of Science, University of Shanghai for Science and Technology, Shanghai, 200093, China;Institute of Applied Mathematics, College of Mathematics and Information Science, Henan University, Kaifeng, 475000, China;Department of Mathematics, Liaocheng University, Liaocheng, 252059, China;Institute of Applied Mathematics, College of Mathematics and Information Science, Henan University, Kaifeng, 475000, China
Venue:
Applied Numerical Mathematics
Year:
2009

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Abstract

A spectral gradient projection algorithm for monotone nonlinear equations with convex constraints is proposed. This new procedure is obtained by combining a modified spectral gradient method and a projection method. A relevant property of the presented method is that the computation of the iteration sequence does not require the solution of any subproblem. The algorithm is shown to be globally convergent under mild assumptions and it can be also applied to nonsmooth equations. Preliminary numerical tests show that the proposed method works quite well even for large scale problems.