Conic Descent Redux for Memory-Efficient Optimization
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.
Cite
@article{arxiv.2308.07343,
title = {Conic Descent Redux for Memory-Efficient Optimization},
author = {Bingcong Li and Georgios B. Giannakis},
journal= {arXiv preprint arXiv:2308.07343},
year = {2023}
}