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Home / Proceedings / Proceedings of the AAAI Conference on Artificial Intelligence, 30 / No. 1: Thirtieth AAAI Conference On Artificial Intelligence

A Proximal Alternating Direction Method for Semi-Definite Rank Minimization

March 8, 2023

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Authors

Ganzhao Yuan

King Abdullah University of Science and Technology (KAUST)


Bernard Ghanem

King Abdullah University of Science and Technology (KAUST)


DOI:

10.1609/aaai.v30i1.10228


Abstract:

Semi-definite rank minimization problems model a wide range of applications in both signal processing and machine learning fields. This class of problem is NP-hard in general. In this paper, we propose a proximal Alternating Direction Method (ADM) for the well-known semi-definite rank regularized minimization problem. Specifically, we first reformulate this NP-hard problem as an equivalent biconvex MPEC (Mathematical Program with Equilibrium Constraints), and then solve it using proximal ADM, which involves solving a sequence of structured convex semi-definite subproblems to find a desirable solution to the original rank regularized optimization problem. Moreover, based on the Kurdyka-Lojasiewicz inequality, we prove that the proposed method always converges to a KKT stationary point under mild conditions. We apply the proposed method to the widely studied and popular sensor network localization problem. Our extensive experiments demonstrate that the proposed algorithm outperforms state-of-the-art low-rank semi-definite minimization algorithms in terms of solution quality.

Topics: AAAI

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HOW TO CITE:

Ganzhao Yuan|| Bernard Ghanem A Proximal Alternating Direction Method for Semi-Definite Rank Minimization Proceedings of the AAAI Conference on Artificial Intelligence, 30 (2016) .

Ganzhao Yuan|| Bernard Ghanem A Proximal Alternating Direction Method for Semi-Definite Rank Minimization AAAI 2016, .

Ganzhao Yuan|| Bernard Ghanem (2016). A Proximal Alternating Direction Method for Semi-Definite Rank Minimization. Proceedings of the AAAI Conference on Artificial Intelligence, 30, .

Ganzhao Yuan|| Bernard Ghanem. A Proximal Alternating Direction Method for Semi-Definite Rank Minimization. Proceedings of the AAAI Conference on Artificial Intelligence, 30 2016 p..

Ganzhao Yuan|| Bernard Ghanem. 2016. A Proximal Alternating Direction Method for Semi-Definite Rank Minimization. "Proceedings of the AAAI Conference on Artificial Intelligence, 30". .

Ganzhao Yuan|| Bernard Ghanem. (2016) "A Proximal Alternating Direction Method for Semi-Definite Rank Minimization", Proceedings of the AAAI Conference on Artificial Intelligence, 30, p.

Ganzhao Yuan|| Bernard Ghanem, "A Proximal Alternating Direction Method for Semi-Definite Rank Minimization", AAAI, p., 2016.

Ganzhao Yuan|| Bernard Ghanem. "A Proximal Alternating Direction Method for Semi-Definite Rank Minimization". Proceedings of the AAAI Conference on Artificial Intelligence, 30, 2016, p..

Ganzhao Yuan|| Bernard Ghanem. "A Proximal Alternating Direction Method for Semi-Definite Rank Minimization". Proceedings of the AAAI Conference on Artificial Intelligence, 30, (2016): .

Ganzhao Yuan|| Bernard Ghanem. A Proximal Alternating Direction Method for Semi-Definite Rank Minimization. AAAI[Internet]. 2016[cited 2023]; .


ISSN: 2374-3468


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