Two restart-free accelerated first-order methods for nonconvex functions with Lipschitz gradients and Hessians achieve O(ε^{-7/4}) complexity by discretizing a new ODE model, with adaptive Lipschitz estimation in one variant.
Taylor, Alexandre d’Aspremont, and Jérôme Bolte
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math.OC 2years
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AAMD combines preconditioning, acceleration, and adaptivity in mirror descent using a Lyapunov budget to achieve O(1/k^2) rates under dual relative smoothness and bounded sublevel sets.
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A Restart-Free Accelerated Algorithm for Non-Convex Minimization: Continuous and Discrete Analysis
Two restart-free accelerated first-order methods for nonconvex functions with Lipschitz gradients and Hessians achieve O(ε^{-7/4}) complexity by discretizing a new ODE model, with adaptive Lipschitz estimation in one variant.
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Adaptive Accelerated Mirror Descent in Primal and Dual Spaces
AAMD combines preconditioning, acceleration, and adaptivity in mirror descent using a Lyapunov budget to achieve O(1/k^2) rates under dual relative smoothness and bounded sublevel sets.