<ul data-eligibleForWebStory="false"><li>This work examines the robustness of different first-order optimization methods in dealing with relative inexactness in gradient computations.</li><li>Three major families of methods analyzed are constant step gradient descent, long-step methods, and accelerated methods.</li><li>Long-step and accelerated methods are theoretically shown to be not robust to inexactness initially.</li><li>A semi-heuristic shortening factor is introduced to enhance the theoretical guarantees of long-step and accelerated methods.</li><li>All methods are tested on an inexact problem, showing that accelerated methods are more robust than expected and the shortening factor helps long-step methods significantly.</li><li>The study concludes that all shortened methods appear promising, even in an inexact setting.</li></ul>

Empirical and computer-aided robustness analysis of long-step and accelerated methods in smooth convex optimization

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