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Multivariate spectral DY-type projection method for convex constrained nonlinear monotone equations. (English) Zbl 1368.49038
Summary: In this paper, we consider a multivariate spectral DY-type projection method for solving nonlinear monotone equations with convex constraints. The search direction of the proposed method combines those of the multivariate spectral gradient method and DY conjugate gradient method. With no need for the derivative information, the proposed method is very suitable to solve large-scale nonsmooth monotone equations. Under appropriate conditions, we prove the global convergence and R-linear convergence rate of the proposed method. The preliminary numerical results also indicate that the proposed method is robust and effective.

49M37 Numerical methods based on nonlinear programming
65H10 Numerical computation of solutions to systems of equations
65K05 Numerical mathematical programming methods
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