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Lyapunov Functions and $R$-Linear Convergence for Quadratic Barzilai-Borwein Dynamics
The Barzilai--Borwein (BB) method is $R$-linearly convergent on strongly convex quadratics, although neither the objective value nor the gradient norm is generally monotone. We construct an explicit current-point Lyapunov function for the quadratic dynamics after the warm-up step, assuming that both
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