We study the second-order feasibility cone for given data (M; g). We construct a new representation for this cone and its dual based on the spectral decomposition of the matrix
This representation is used to efficiently solve the problem of projecting an arbitrary point
which aside from theoretical interest also arises as a necessary subroutine in the re-scaled perceptron algorithm. We develop a method for solving the projection problem to an accuracy
whose computational complexity is bounded by
operations after the spectral decomposition of
is computed. Here the width
width
denotes the widths of
, respectively. This is a substantial improvement over the complexity of a generic interior-point method.
By: Alexandre Belloni; Robert M. Freund
Published in: RC24072 in 2006
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