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Spectral modified Polak-Ribiére-Polyak projection conjugate gradient method for solving monotone systems of nonlinear equations. (English) Zbl 1433.65109
Summary: In this paper, we present a modification of Polak-Ribiére-Polyak (PRP) conjugate gradient method for solving system of monotone nonlinear equations which is a combination of spectral conjugate gradient method and the hyperplane projection technique. The method is based on two methods for unconstrained optimization proposed by Z. Wan et al. [Appl. Math. Lett. 24, No. 1, 16–22 (2011; Zbl 1208.49039)] and X. Sun [Int. J. Adv. Appl. Math. Mech. 2, No. 3, 51–59 (2015; Zbl 1359.90154)]. We obtain a new search direction by the use of a different formula for the conjugate gradient parameter. The search direction satisfies the sufficient descent condition and the global convergence of the method is established under some assumptions. Preliminary numerical comparison with some existing methods shows the efficiency of the proposed method.
MSC:
65K05 Numerical mathematical programming methods
90C06 Large-scale problems in mathematical programming
90C56 Derivative-free methods and methods using generalized derivatives
65H10 Numerical computation of solutions to systems of equations
90C30 Nonlinear programming
90C53 Methods of quasi-Newton type
65K10 Numerical optimization and variational techniques
Software:
MCPLIB
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References:
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