In this paper, we propose a large-update interior-point algorithm for linear optimization based on a new kernel function. New search directions and proximity measure are defined based on this kernel function. We show that if a strictly feasible starting point is available, then the new algorithm has O(3/4log n/?) iteration complexity.

This paper concerns an extension of the arc-search strategy that was proposed by Yang [26] for linear optimization to semidefinite optimization case. Based on the Nesterov-Todd direction as Newton search direction it is shown that the complexity bound of the proposed algorithm is of the same order as that of the corresponding algorithm for linear optimization. Some preliminary numerical results indicate that our primal-dual arc-search path-following method is promising for solving the semidefinite optimization problems.2010 Mathematics Subject Classification. 90C51.

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