Please use this identifier to cite or link to this item:
https://hdl.handle.net/10316/44191
Title: | Positive semidefinite rank | Authors: | Fawzi, Hamza Gouveia, João Parrilo, Pablo A. Robinson, Richard Z. Thomas, Rekha R. |
Issue Date: | 2015 | Publisher: | Springer | Project: | info:eu-repo/grantAgreement/FCT/5876/147205/PT | Serial title, monograph or event: | Mathematical Programming | Volume: | 153 | Issue: | 1 | Abstract: | Let M∈R^p×q be a nonnegative matrix. The positive semidefinite rank (psd rank) of M is the smallest integer k for which there exist positive semidefinite matrices A_i, B_j of size k × k such that M_ij = trace(A_i B_j). The psd rank has many appealing geometric interpretations, including semidefinite representations of polyhedra and information-theoretic applications. In this paper we develop and survey the main mathematical properties of psd rank, including its geometry, relationships with other rank notions, and computational and algorithmic aspects. | URI: | https://hdl.handle.net/10316/44191 | DOI: | 10.1007/s10107-015-0922-1 10.1007/s10107-015-0922-1 |
Rights: | embargoedAccess |
Appears in Collections: | I&D CMUC - Artigos em Revistas Internacionais |
Files in This Item:
File | Description | Size | Format | |
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survey.pdf | 2.35 MB | Adobe PDF | View/Open |
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