A Centered Projective Algorithm for Linear Programming

We describe a projective algorithm for linear programming that shares features with Karmarkar's projective algorithm and its variants and with the path-following methods of Gonzaga, Kojima-Mizuno-Yoshise, Monteiro-Adler, Renegar, Vaidya and Ye. It operates in a primal-dual setting, stays close to the central trajectories, and converges in O√n L iterations like the latter methods. Here n is the number of variables and L the input size of the problem. However, it is motivated by seeking reductions in a suitable potential function as in projective algorithms, and the approximate centering is an automatic byproduct of our choice of potential function.

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