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Accelerated Gradient Methods via Inertial Systems with Hessian-driven Damping
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We analyze the convergence rate of a family of inertial algorithms, which can be obtained by discretization of an inertial system with Hessian-driven damping. We recover a convergence rate, up to a factor of 2 speedup upon Nesterov's scheme, for smooth strongly convex functions. As a byproduct of our analyses, we also derive linear convergence rates for convex functions satisfying quadratic growth condition or Polyak-\L ojasiewicz inequality. As a significant feature of our results, the dependence of the convergence rate on parameters of the inertial system/algorithm is revealed explicitly. This may help one get a better understanding of the acceleration mechanism underlying an inertial algorithm.
Forward citations
Cited by 2 Pith papers
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Heavy-ball dynamics with Hessian-driven damping for non-convex optimization under the {\L}ojasiewicz condition
For non-convex objectives satisfying the Łojasiewicz inequality of order 2, the DIN continuous-time dynamics converge in function value at a rate arbitrarily close to e^{-2√µ t}, which is worst-case optimal within thi...
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Inertial Primal Dual Dynamics with Hessian-driven Damping for Saddle Point Problems
New inertial primal-dual ODEs with Hessian damping achieve O(1/t²) convex rates and O(1/t^{α−1}) strongly-convex rates without knowing the strong convexity moduli.
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