Semidefinite programming: Difference between revisions

Revision as of 22:24, 26 February 2022

Revision as of 08:46, 20 March 2022

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=== Interior point methods ===

Most codes are based on [[interior point methods]] (CSDP, [[MOSEK]], SeDuMi, [https://www.math.cmu.edu/~reha/sdpt3.html SDPT3], DSDP, SDPA). Robust and efficient for general linear SDP problems. Restricted by the fact that the algorithms are second-order methods and need to store and factorize a large (and often dense) matrix. Theoretically, the state-of-the-art high-accuracy SDP algorithms<ref>{{Cite journal |last=Jiang |first=Haotian |last2=Kathuria |first2=Tarun |last3=Lee |first3=Yin Tat |last4=Padmanabhan |first4=Swati |last5=Song |first5=Zhao |date=November 2020 |title=A Faster Interior Point Method for Semidefinite Programming |url=https://ieeexplore.ieee.org/document/9317892/ |journal=2020 IEEE 61st Annual Symposium on Foundations of Computer Science (FOCS) |___location=Durham, NC, USA |publisher=IEEE |pages=910–918 |doi=10.1109/FOCS46700.2020.00089 |isbn=978-1-7281-9621-3}}</ref><ref>{{Cite journalarXiv |last=Huang |first=Baihe |last2=Jiang |first2=Shunhua |last3=Song |first3=Zhao |last4=Tao |first4=Runzhou |last5=Zhang |first5=Ruizhe |date=2021-11-18 |title=Solving SDP Faster: A Robust IPM Framework and Efficient Implementation |url=http://arxiv.org/abs/2101.08208 |journal=arXiv:2101.08208 [cs, math] |doi=10.48550/arxiv.2101.08208}}</ref> are based on this approach.

=== First-order methods ===