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A RELAXED VECTOR AUXILIARY VARIABLE ALGORITHM FOR UNCONSTRAINED OPTIMIZATION PROBLEMS
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DOI：10.1137/23M1611087.png)
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Abstract
En 中文
We present a novel optimization algorithm, a relaxed vector auxiliary variable (RVAV), 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 superlinear in the univariate case. We also propose an adaptive version of RVAV with Steffensen step size. We validate the robustness and fast convergence of our algorithm through ample numerical experiments.
Keywords:
Key words. optimization
gradient descent
machine learning
SAV
adaptive learning rate
Journal
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