Proves weak convergence of Nesterov accelerated primal-dual trajectories to primal-dual solutions for alpha >=3 without Lipschitz gradient assumption, plus o(t^{-2}) rates for alpha>3, using Bregman distances in finite dimensions.
The iterates of Nesterov's accelerated algorithm converge in the critical regimes , year =
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There exists a differentiable convex potential in R^2 such that the Nesterov ODE converges to the minimizer along a trajectory of infinite path length.
Accelerated augmented Lagrangian schemes for convex linearly constrained problems achieve o(1/k^2) rates on feasibility violation and objective residual plus iterate convergence under critical parameters.
APAPC integrates Nesterov acceleration into primal-dual forward-backward schemes by exploiting dual strong convexity to achieve optimal sublinear and accelerated linear convergence rates.
Proves convergence to saddle points and o(1/t²) gap rates for continuous-time dynamics with α/t damping (α≥3) and for a structure-preserving discretization under a t_k sequence condition with ρ≤1.
The accelerated backward-forward method achieves O(1/k²) convergence on convex composite problems and accelerated linear convergence when the smooth component is strongly convex.
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Trajectory convergence and $o(t^{-2})$ rates for Nesterov accelerated primal-dual dynamics without Lipschitz gradient assumption
Proves weak convergence of Nesterov accelerated primal-dual trajectories to primal-dual solutions for alpha >=3 without Lipschitz gradient assumption, plus o(t^{-2}) rates for alpha>3, using Bregman distances in finite dimensions.
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Nesterov Flow May Travel Infinitely Long to Converge to a Minimizer
There exists a differentiable convex potential in R^2 such that the Nesterov ODE converges to the minimizer along a trajectory of infinite path length.
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Convergence of iterates and improved rates for accelerated augmented Lagrangian methods for linearly constrained convex optimization
Accelerated augmented Lagrangian schemes for convex linearly constrained problems achieve o(1/k^2) rates on feasibility violation and objective residual plus iterate convergence under critical parameters.
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A Nesterov-Accelerated Primal-Dual Splitting Algorithm for Convex Nonsmooth Optimization
APAPC integrates Nesterov acceleration into primal-dual forward-backward schemes by exploiting dual strong convexity to achieve optimal sublinear and accelerated linear convergence rates.
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Fast primal-dual methods for convex-concave bilinear saddle point problems: continuous-time dynamics and discrete algorithms
Proves convergence to saddle points and o(1/t²) gap rates for continuous-time dynamics with α/t damping (α≥3) and for a structure-preserving discretization under a t_k sequence condition with ρ≤1.
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Accelerated Backward Forward Method for Convex Optimization
The accelerated backward-forward method achieves O(1/k²) convergence on convex composite problems and accelerated linear convergence when the smooth component is strongly convex.