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A Polynomial Arc-Search Interior-Point Algorithm for Linear Programming

Yaguang Yang(yaguang.yang***at***verizon.net)

Abstract: In this paper, ellipse is used to approximate the central path of the linear programming. An interior-point algorithm is devised to search the optimizers along the ellipse. The algorithm is proved to be polynomial with the complexity bound $O(n^{\frac{1}{2}}\log(1/\epsilon))$. Numerical test is conducted for problems in Netlib. For most tested Netlib problems, the result shows that the new algorithm uses less iteration to converge than the Matlab optimization toolbox {\tt linprog} which implements the state-of-art Mehrotra's predictor-corrector algorithm. For all the tested problems, the number of total iterations using the new algorithm is about 20$\%$ fewer than the one using {\tt linprog}.

Keywords: Arc-search, interior-point method, polynomial algorithm, linear programming.

Category 1: Linear, Cone and Semidefinite Programming (Linear Programming )


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Entry Submitted: 11/27/2010
Entry Accepted: 12/02/2010
Entry Last Modified: 11/27/2010

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