Abstract
In this paper, we analyze a feasible predictor-corrector linear programming variant of Mehrotra's algorithm. The analysis is done in the negative infinity neighborhood of the central path. We demonstrate the theoretical efficiency of this algorithm by showing its polynomial complexity. The complexity result establishes an improvement of factor $ n^3 $ in the theoretical complexity of an earlier presented variant in [2], which is a huge improvement. We examine the performance of our algorithm by comparing its implementation results to solve some NETLIB problems with the algorithm presented in [2].
Highlights
Karmarkarâs publication [11] which appeared in 1984, meant a great moving forward in the area of optimization algorithms
Mizuno and Yoshise [12] developed the first primal-dual path-following method. Their method works in the way that, at each iteration, the iterates are allowed to be located in a wide neighborhood of the so-called central path
They take only a single Newton step to do that. They were able to obtain an O complexity bound for a linear programming (LP) with n nonnegative variables and integer data with length L
Summary
Karmarkarâs publication [11] which appeared in 1984, meant a great moving forward in the area of optimization algorithms. In [20], the authors have shown by a numerical example that a feasible version of the algorithm may be forced to make many small steps This motivated them to introduce certain safeguards, that allowed them to prove polynomial iteration complexity. Almeida and Teixeira [2] have presented a predictor-corrector interior-point algorithm for LP, based on the negative infinity wide neighborhood. They established the complexity bound O n4 |log Δ| for their algorithm and they proved its superlinear convergence.
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