Work

Nesterov Acceleration with Operator Decomposition

Year: 2026

Type: preprint

Abstract: We propose Nesterov acceleration with Operator Decomposition (NOD), which extends Nesterov's accelerated gradient descent (NAG) from smooth strongly convex optimization to the broader setting of strongly monotone, Lipschitz operators. The key insight is to decompose the operator into cyclically monotone and monotone components, with the Asplund decomposition providing the tightest such representation, and to have the algorithm utilize the decomposed oracles. NOD and its analysis subsume the classical theory of Nesterov acceleration and yield an iteration complexity for finding an $ε$-accurate solution of \[ Θ\left(\sqrt{\frac{L_ϕ}μ + \frac{L_{\mathbb{S}}^2}{μ^2}} \,\log \frac{1}ε\right), \] where $μ$ is the strong monotonicity parameter, $L_ϕ$ is the Lipschitz constant of the cyclically monotone component, and $L_{\mathbb{S}}$ is the Lipschitz constant of the (possibly acyclic) monotone remainder.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2604.11105

Authors: Lee, Jaewook, Ryu, Ernest K., Yun, Chulhee

Institutions: Stanford University, University of California, Los Angeles, Korea Advanced Institute of Science and Technology

Topic: Optimization and Variational Analysis

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, National Research Foundation, National Research Foundation of Korea, Korea Advanced Institute of Science and Technology, Ministry of Science and ICT, South Korea

Awards: G3812690899, Collaborative Research: CIF: Medium: Post-Modern Min-Max Optimization Theory: Departure from Classical Minimization Theory

OpenAlex ID: W7154422149

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