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arXiv · 2308.07343

Conic Descent Redux for Memory-Efficient Optimization

Bingcong Li·Georgios B. Giannakis
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Abstract

Conic programming has well-documented merits in a gamut of signal processing and machine learning tasks. This contribution revisits a recently developed first-order conic descent (CD) solver, and advances it in three aspects: intuition, theory, and algorithmic implementation. It is found that CD can afford an intuitive geometric derivation that originates from the dual problem. This opens the door to novel algorithmic designs, with a momentum variant of CD, momentum conic descent (MOCO) exemplified. Diving deeper into the dual behavior CD and MOCO reveals: i) an analytically justified stopping criterion; and, ii) the potential to design preconditioners to speed up dual convergence. Lastly, to scale semidefinite programming (SDP) especially for low-rank solutions, a memory efficient MOCO variant is developed and numerically validated.

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Bingcong Li, Georgios B. Giannakis. 2023-08-13. Conic Descent Redux for Memory-Efficient Optimization. https://arxiv.org/abs/2308.07343

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