Primal-dual interior-point algorithm for convex quadratic semi-definite optimization

Abstract In this paper, we present a new primal-dual interior-point algorithm for solving a special case of convex quadratic semi-definite optimization based on a parametric kernel function. The proposed parametric kernel function is used both for determining the search directions and for measuring the distance between the given iterate and the μ -center for the algorithm. These properties enable us to derive the currently best known iteration bounds for the algorithm with large- and small-update methods, namely, O ( n log n log n e ) and O ( n log n e ) , respectively, which reduce the gap between the practical behavior of the algorithm and its theoretical performance results.

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