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The convergence properties of some new conjugate gradient methods. (English) Zbl 1116.65073
A new conjugate gradient formula $\beta^*_k$ is given to compute the search directions for unconstrained optimization problems. General convergence results for the proposed formula with exact Wolfe-Powell line search and Grippo-Lucidi line search. Under these line searches and some assumptions, the global convergence properties of the given methods are discussed. The given formula $\beta^*_k\ge 0$ has the similar form as $\beta^{PRP}_k$. Some numerical results show that the proposed methods are efficient.

65K05Mathematical programming (numerical methods)
90C59Approximation methods and heuristics
90C30Nonlinear programming
Full Text: DOI
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