What does this research mean for the field?

An adaptive accelerated gradient method using local estimation of the smoothness constant achieves a convergence rate of O(1/k^2) for smooth convex functions and a linear rate for strongly convex functions without requiring line search or knowledge of the strong convexity parameter. Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

To develop an adaptive accelerated gradient optimization method for smooth convex problems that operates without requiring line search routines or prior knowledge of smoothness parameters.

August 22, 2026Journal of Optimization Theory and ApplicationsOpen Access

Adaptive Accelerated Gradient Method for Smooth Convex Optimization

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Authors

ZWZepeng WangUniversity of Groningen JPJuan PeypouquetUniversity of Groningen

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Implication

Algorithm analysis demonstrates an adaptive accelerated gradient method achieves fast convergence without line searches, indicating high computational efficiency.

Key Points

To develop an adaptive accelerated gradient optimization method for smooth convex problems that operates without requiring line search routines or prior knowledge of smoothness parameters.
Designed an accelerated gradient algorithm incorporating adaptive step-size selection based on local estimation of the unknown smoothness constant.
Formulated the convergence framework without relying on line search checks or explicit knowledge of the strong convexity parameter.
Proved weak convergence of the iterate sequence to a minimizer with an accelerated objective function convergence rate of O(1/k^2).
Demonstrated that for strongly convex objectives, the function values converge at a linear rate of O((1/k^2)(1-rho)^k), where rho = O(mu/L).

Cite This Study

Wang et al. (2026) studied this question.

synapsesocial.com/papers/6a895e6bca7ade938187c8bf https://doi.org/10.1007/s10957-026-03086-z

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Implication

Algorithm analysis demonstrates an adaptive accelerated gradient method achieves fast convergence without line searches, indicating high computational efficiency.

Adaptive Accelerated Gradient Method for Smooth Convex Optimization

Discussion

Member takes

Implication

Key Points

Cite This Study

Adaptive Accelerated Gradient Method for Smooth Convex Optimization

Discussion

Member takes

Implication

Key Points

Cite This Study

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