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Takashi Tsuchiya (tsuchiyasun312.ism.ac.jp) Abstract: The problem of maximizing the sum of linear functional and several weighted logarithmic determinant (logdet) functions under semidefinite constraints is a generalization of the semidefinite programming (SDP) and has a number of applications in statistics and datamining, and other areas of informatics and mathematical sciences. In this paper, we extend the framework of standard primaldual pathfollowing algorithms for SDP to this problem. Employing this framework, we show that the longstep pathfollowing algorithm analogous to the one in SDP has ${\cal O}(N\log(1/\varepsilon)+N)$ iterationcomplexity to reduce the duality gap by a factor of $\varepsilon$, where $N = \sum N_i$, where $N_i$ is the size of the $i$th positive semidefinite matrix block which is assumed to be an $N_i\times N_i$ matrix. Keywords: determinant maximization problem, logarithmic determinant function, semidefinite programming, primaldual interiorpoint algorithm Category 1: Linear, Cone and Semidefinite Programming Citation: Research Memorandum No. 980, The Institute of Statistical Mathematics, 467 MinamiAzabu, Minatoku, Tokyo 1068569, JAPAN, February 2006 Download: [PDF] Entry Submitted: 02/04/2006 Modify/Update this entry  
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