A new stepsize for gradient method via weak secant equation

In this work we present a new technique for stepsize selection in the frame of gradient method. This new stepsize selection technique provides a different stepsize for every component of the negative gradient search. The algorithm then selects the stepsizes along the negative gradient using a new approximation of the Hessian based on the weak secant equation. The resulting algorithm belongs to the same class of gradient methods with linear convergence property. Some preliminary numerical results suggest that the algorithm compares favourably with the Barzilai-Borwein method.

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