Primal–dual path-following algorithms for determinant maximization problems with linear matrix inequalities

Primal–dual path-following algorithms are considered for determinant maximization problem (maxdet-problem). These algorithms apply Newton's method to a primal–dual central path equation similar to that in semidefinite programming (SDP) to obtain a Newton system which is then symmetrized to avoid nonsymmetric search direction. Computational aspects of the algorithms are discussed, including Mehrotra-type predictor–corrector variants. Focusing on three different symmetrizations, which leads to what are known as the AHO, H..K..M and NT directions in SDP, numerical results for various classes of maxdet-problem are given. The computational results show that the proposed algorithms are efficient, robust and accurate.