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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

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.

MSC:

65K05 Numerical mathematical programming methods
90C22 Semidefinite programming
90C51 Interior-point methods
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