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We review the basic algorithms using the gradient direction for unconstrained QP problems, discuss their convergence in Euclidean and energy norm, and examine the effect of the steplength on their performance. We pay special attention to the possibility of enhancing the information from the previous step via the steplength (the Barizilai–Borwein method) or momentum (Polyak’s heavy ball method).

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Gradient Methods

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  • 发表日期：

    2025年

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  • Zdeněk Dostál

摘要

We review the basic algorithms using the gradient direction for unconstrained QP problems, discuss their convergence in Euclidean and energy norm, and examine the effect of the steplength on their performance. We pay special attention to the possibility of enhancing the information from the previous step via the steplength (the Barizilai–Borwein method) or momentum (Polyak’s heavy ball method).