## 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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### References:

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