Approximate Analytic Center Quadratic Cut Method for Strongly Monotone Variational Inequalities
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چکیده
For strongly monotone variational inequality problems (VIP) convergence of an algorithm is investigated which, at each iteration k, adds a quadratic cut through an approximate analytic center xk of the subsequently shrinking convex body. First it is shown that the sequence of xk converges to the unique solution x ∗ of the VIP at O(1/ √ k). As an interesting detail note that — for increasingly accurate analytic centers — the complexity constants converge to the quantities obtained for ACQCM with exact centers. Secondly we show that the arithmetic complexity to update from xk to xk+1 after inserting a quadratic cut through xk is bounded by a constant number of Newton iterations plus O(n · ln ln[ζ · k 2 ε4 ]), where n is the space-dimension, ε is the final solution accuracy ‖xk − x∗‖, and ζ depends on some problem-specific constants only.
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تاریخ انتشار 2001