A Note on Quadratic Convergence of the Homogeneous and Self-Dual Linear Programming Algorithm
نویسندگان
چکیده
In this note we show that Ye-Todd-Mizuno's O(p nL)-iteration homogeneous and self-dual linear programming (LP) algorithm possesses quadratic convergence of the duality gap to zero. In the case of infeasibility, this result shows that a homogenizing variable quadratically converges to zero and implies that the iterates of the (original) LP variable quadratically diverge. Thus, we have established a complete asymptotic convergence result for interior-point algorithms without any assumption on the LP problem.
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