On the Second-Order Feasibility Cone: Primal-Dual Representation and Efficient Projection

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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