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• W2065110770 abstract "We build upon the work of Fukuda et al. [SIAM J. Optim., 11 (2001), pp. 647--674] and Nakata et al. [Math. Program., 95 (2003), pp. 303--327], in which the theory of partial positive semidefinite matrices was applied to the semidefinite programming (SDP) problem as a technique for exploiting sparsity in the data. In contrast to their work, which improved an existing algorithm based on a standard search direction, we present a primal-dual path-following algorithm that is based on a new search direction, which, roughly speaking, is defined completely within the space of partial symmetric matrices. We show that the proposed algorithm computes a primal-dual solution to the SDP problem having duality gap less than a fraction $varepsilon > 0$ of the initial duality gap in ${cal O}(n log(varepsilon^{-1}))$ iterations, where n is the size of the matrices involved. Moreover, we present computational results showing that the algorithm possesses several advantages over other existing implementations." @default.
• W2065110770 created "2016-06-24" @default.
• W2065110770 creator A5002663715 @default.
• W2065110770 date "2003-01-01" @default.
• W2065110770 modified "2023-09-25" @default.
• W2065110770 title "Semidefinite Programming in the Space of Partial Positive Semidefinite Matrices" @default.
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• W2065110770 doi "https://doi.org/10.1137/s105262340240851x" @default.
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