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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 \(\beta^*_k\geq 0\) has the similar form as \(\beta^{PRP}_k\). Some numerical results show that the proposed methods are efficient.

MSC:
65K05 Numerical mathematical programming methods
90C59 Approximation methods and heuristics in mathematical programming
90C30 Nonlinear programming
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