An adaptive descent extension of the Polak–Rebière–Polyak conjugate gradient method based on the concept of maximum magnification

Iranian Journal of Numerical Analysis and Optimization

مقاله 11، دوره 11، شماره 1 - شماره پیاپی 19، خرداد 2021، صفحه 211-219   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2021.67048.0

نویسندگان

Z. Aminifard^* ؛ S. Babaie-Kafaki

Department of Mathematics, Semnan University, P.O. Box: 35195–363, Semnan, Iran.

چکیده

Recently, a one-parameter extension of the Polak–Rebière–Polyak method has been suggested, having acceptable theoretical features and promising numerical behavior. Here, based on an eigenvalue analysis on the method with the aim of avoiding a search direction in the direction of the maximum magnification by a symmetric version of the search direction matrix, an adaptive formula for computing parameter of the method is proposed. Under standard assumptions, the given formula ensures the sufficient descent property and guarantees the global convergence of the method. Numerical experiments are done on a collection of CUTEr test problems. They show practical effectiveness of the suggested formula for the parameter of the method.

کلیدواژه‌ها

Unconstrained optimization؛ Conjugate gradient method؛ Maximum magnification؛ Line search

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