Accelerating semidefinite programming beyond limit: ADMM with tune-free operator stepsize

Yifan Ran

Keywords: semidefinite programming, scalability, alternating direction method of multipliers, tune-free operator stepsize

TL;DR: We significantly alleviate the long-standing scalability issue of semidefinite programming.

Abstract: In this work, we significantly alleviate the long-standing scalability issue of semidefinite programming (SDP), by equipping a novel tune-free operator stepsize to the alternating direction method of multipliers (ADMM) optimizer. To our best knowledge, this is the first operator stepsize in the context of SDP. More importantly, it is tune-free and computationally cheap (defined on dot product). Preliminary tests show that our operator ADMM surpasses the acceleration limit of the standard scalar version (limit found via grid search), i.e., our operator stepsize can outperform an arbitrarily fine tuned scalar one.

Primary Area: optimization

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Submission Number: 9651