An Element-wise RSAV Algorithm for Unconstrained Optimization Problems

• URL: http://arxiv.org/abs/2309.04013v1
• Date: Thu, 7 Sep 2023 20:37:23 GMT
• Title: An Element-wise RSAV Algorithm for Unconstrained Optimization Problems
• Authors: Shiheng Zhang, Jiahao Zhang, Jie Shen and Guang Lin
• Abstract summary: We present a novel optimization algorithm, element-wise relaxed scalar auxiliary variable (E-RSAV) Our algorithm features rigorous proofs of linear convergence in the convex setting. We also propose an adaptive version of E-RSAV with Steffensen step size.
• Score: 13.975774245256561
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We present a novel optimization algorithm, element-wise relaxed scalar auxiliary variable (E-RSAV), that satisfies an unconditional energy dissipation law and exhibits improved alignment between the modified and the original energy. Our algorithm features rigorous proofs of linear convergence in the convex setting. Furthermore, we present a simple accelerated algorithm that improves the linear convergence rate to super-linear in the univariate case. We also propose an adaptive version of E-RSAV with Steffensen step size. We validate the robustness and fast convergence of our algorithm through ample numerical experiments.

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