- An extension of the standard polynomial-time primal-dual path-following algorithm to the weighted determinant maximization problem with semidefinite constraints Takashi Tsuchiya (tsuchiyasun312.ism.ac.jp) Yu Xia (yuxiaism.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 primal-dual path-following algorithms for SDP to this problem. Employing this framework, we show that the long-step path-following algorithm analogous to the one in SDP has ${\cal O}(N\log(1/\varepsilon)+N)$ iteration-complexity 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, primal-dual interior-point algorithm Category 1: Linear, Cone and Semidefinite Programming Citation: Research Memorandum No. 980, The Institute of Statistical Mathematics, 4-6-7 Minami-Azabu, Minato-ku, Tokyo 106-8569, JAPAN, February 2006 Download: [PDF]Entry Submitted: 02/04/2006Entry Accepted: 02/04/2006Entry Last Modified: 02/04/2006Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Programming Society and by the Optimization Technology Center.