mlsanityData to 14 Oct 2026

Optimizing the Efficiency of First-Order Methods for Decreasing the Gradient of Smooth Convex Functions

arXiv 1803.06600 ↗First posted 18 Mar 2018math.OCcited by 14

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Abstract (arXiv)

This paper optimizes the step coefficients of first-order methods for smooth convex minimization in terms of the worst-case convergence bound (i.e., efficiency) of the decrease in the gradient norm. This work is based on the performance estimation problem approach. The worst-case gradient bound of the resulting method is optimal up to a constant for large-dimensional smooth convex minimization problems, under the initial bounded condition on the cost function value. This paper then illustrates that the proposed method has a computationally efficient form that is similar to the optimized gradient method.

Key facts. Cited by 14 papers in the map (data through 14 Oct 2026). First posted on arXiv 18 Mar 2018.

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Citing papers per year: 2021: 3; 2022: 5; 2023: 3; 2024: 3.

14 papers.

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  1. 2023Provably Faster Gradient Descent via Long Stepscited by 20
  2. 2022Communication Acceleration of Local Gradient Methods via an Accelerated Primal-Dual Algorithm with Inexact Proxcited by 19
  3. 2022PEPit: computer-assisted worst-case analyses of first-order optimization methods in Pythoncited by 11
  4. 2023Accelerating Value Iteration with Anchoringcited by 11
  5. 2022Optimal Gradient Sliding and its Application to Distributed Optimization Under Similaritycited by 10
  6. 2022Smooth Monotone Stochastic Variational Inequalities and Saddle Point Problems: A Surveycited by 10
  7. 2021Complementary Composite Minimization, Small Gradients in General Norms, and Applicationscited by 9
  8. 2024Projected gradient methods for nonconvex and stochastic smooth optimization: new complexities and auto-conditioned stepsizescited by 6
  9. 2021Potential Function-based Framework for Making the Gradients Small in Convex and Min-Max Optimizationcited by 4
  10. 2021Practical Schemes for Finding Near-Stationary Points of Convex Finite-Sumscited by 4
  11. 2024SPAM: Stochastic Proximal Point Method with Momentum Variance Reduction for Non-convex Cross-Device Federated Learningcited by 3
  12. 2023DualFL: A Duality-based Federated Learning Algorithm with Communication Acceleration in the General Convex Regimecited by 2
2 more
  1. 2024Optimal Data Splitting in Distributed Optimization for Machine Learningcited by 1
  2. 2022An Optimal Algorithm for Strongly Convex Min-min Optimizationcited by 0