Tsuchiya, Takashi; Xia, Yu An extension of the standard polynomial-time primal-dual path-following algorithm to the weighted determination maximization problem with semidefinite contstraints. (English) Zbl 1137.65044 Pac. J. Optim. 3, No. 1, 165-182 (2007). The authors study the problem of maximizing the sum of a linear function with weighted logdet functions (logarithmic determinants), where the constraints are semidefinite in nature. The article begins with an introductory section containing a brief overview of the literature followed with a section on the weighted determinant maximization problem and the associated central trajectory and its neighborhoods. Several relevant theorems are presented and proven, and the section concludes with a description of the path-following algorithm that can be used for the problem studied in this paper. The last part of the article includes a section on the properties of the proposed algorithm and a discussion of the contribution of this interesting paper. The article concludes with an appendix containing proofs of some lemmas contained in the paper and a list of relevant references. Reviewer: Efstratios Rappos (Athens) Cited in 1 Document MSC: 65K05 Numerical mathematical programming methods 90C22 Semidefinite programming 90C51 Interior-point methods Keywords:semidefinite programming; logarithmic determinant function; primal-dual algorithm; interior point method; max logdet problem PDFBibTeX XMLCite \textit{T. Tsuchiya} and \textit{Y. Xia}, Pac. J. Optim. 3, No. 1, 165--182 (2007; Zbl 1137.65044)