Complexity of the primal-dual path-following algorithms for the weighted determinant maximization problems with linear matrix inequalities in the narrow neighbourhood

摘要

Weighted determinant maximization with linear matrix inequality constraints (maxdet-problem) is a generalization of the semidefinite programming. We give a polynomial-time complexity analysis for the path-following interior-point short-step and predictor-corrector methods for the maxdet-problem based on symmetric Newton equations for certain classes of scaling matrices.