Primal-Dual Path-Following Algorithms for Determinant Maximization Problems With Linear Matrix Inequalities

Authors:
Kim-Chuan Toh
Affiliations:
Department of Mathematics, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260. mattohkc@math.nus.edu.sg
Venue:
Computational Optimization and Applications
Year:
1999

Citing 12
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Abstract

Primal-dual path-following algorithms are considered for determinant maximization problem (maxdet-problem). These algorithms apply Newton‘s method to aprimal-dual central path equation similar to that in semidefiniteprogramming (SDP) to obtain a Newton system which is thensymmetrized to avoid nonsymmetric search direction. Computational aspects of the algorithms are discussed, includingMehrotra-type predictor-corrector variants. Focusing on three different symmetrizations, which leads to what are knownas the AHO, H..K..M and NT directions in SDP, numericalresults for various classes of maxdet-problem are given. The computational results show that the proposed algorithmsare efficient, robust and accurate.