Abstract
Interior point methods for semidefinite programming have recently been studied intensively, due to their polynomial complexity and practical efficiency. Most of these methods are extensions of linear programming algorithms. The primal-dual central path following method for linear programming by Jansen et al. [6] has recently been extended to semidefinite programming by Jiang [7], utilizing the Nesterov-Todd direction and introducing a new distance measure. In this note we refine and extend this analysis: A weaker condition for a feasible full Newton step is established, and quadratic convergence to target points on the central path is shown. Moreover, we show how to compute large dynamic target updates which still allow full Newton steps.
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de Klerk, E., Roos, C., Terlaky, T. (1998). On Primal—Dual Path—Following Algorithms for Semidefinite Programming. In: Giannessi, F., Komlósi, S., Rapcsák, T. (eds) New Trends in Mathematical Programming. Applied Optimization, vol 13. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-2878-1_11
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DOI: https://doi.org/10.1007/978-1-4757-2878-1_11
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