A Lyapunov framework yields O(1/log T) and O(log T/T) gradient-norm rates for Schedule-Free on smooth nonconvex objectives, with the faster rate depending on an unproven assumption.
Global convergence of the Heavy-ball method for convex optimization
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This paper establishes global convergence and provides global bounds of the convergence rate of the Heavy-ball method for convex optimization problems. When the objective function has Lipschitz-continuous gradient, we show that the Cesaro average of the iterates converges to the optimum at a rate of $O(1/k)$ where k is the number of iterations. When the objective function is also strongly convex, we prove that the Heavy-ball iterates converge linearly to the unique optimum.
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Analysis of Schedule-Free Nonconvex Optimization
A Lyapunov framework yields O(1/log T) and O(log T/T) gradient-norm rates for Schedule-Free on smooth nonconvex objectives, with the faster rate depending on an unproven assumption.