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This is a Quantitative Study study.

September 24, 2025Open Access

On Convergence and Stability of Two Extended BB-like Step Sizes

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Proposed new gradient step sizes achieve R-linear convergence in convex optimization, highlighting stability differences.

The new gradient step sizes lead to R-linear convergence in strictly convex quadratic optimization problems, enhancing the Barzilai-Borwein method.
The analysis reveals that the longer step size is stable under certain conditions, while the shorter step size results in instability.
Employing difference equations, convergence and stability are analyzed for two proposed gradient descent methods.
Numerical results substantiate the stability theories, indicating the importance of step size selection in optimization.

Xin Xu (2025) studied this question.

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