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Register a new userOn a Faster $R$-Linear Convergence Rate of the Barzilai-Borwein Method
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Added by
Dawei Li
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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The Barzilai-Borwein (BB) method has demonstrated great empirical success in nonlinear optimization. However, the convergence speed of BB method is not well understood, as the known convergence rate of BB method for quadratic problems is much worse than the steepest descent (SD) method. Therefore, there is a large discrepancy between theory and practice. To shrink this gap, we prove that the BB method converges $R$-linearly at a rate of $1-1/kappa$, where $kappa$ is the condition number, for strongly convex quadratic problems. In addition, an example with the theoretical rate of convergence is constructed, indicating the tightness of our bound.
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