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New spectral PRP conjugate gradient method for unconstrained optimization. (English) Zbl 1208.49039

Summary: A new spectral PRP conjugate gradient algorithm is developed for solving unconstrained optimization problems, where the search direction is a kind of combination of the gradient and the obtained direction, and the steplength is obtained by the Wolfe-type inexact line search. It is proved that the search direction at each iteration is a descent direction of the objective function. Under mild conditions, we establish a global convergence theorem of the proposed method. Numerical results show that the algorithm is promising, compared with existing methods.

MSC:

49M37 Numerical methods based on nonlinear programming
90C52 Methods of reduced gradient type
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