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Two modified hybrid conjugate gradient methods based on a hybrid secant equation. (English) Zbl 1264.49034

Summary: Taking advantage of the attractive features of Hestenes-Stiefel and Dai-Yuan conjugate gradient methods, we suggest two globally convergent hybridizations of these methods following Andrei’s approach of hybridizing the conjugate gradient parameters convexly and Powell’s approach of nonnegative restriction of the conjugate gradient parameters. In our methods, the hybridization parameter is obtained based on a recently proposed hybrid secant equation. Numerical results demonstrating the efficiency of the proposed methods are reported.

MSC:

49M37 Numerical methods based on nonlinear programming
65K05 Numerical mathematical programming methods
90C53 Methods of quasi-Newton type
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