A Full-Newton Step Infeasible Interior-Point Algorithm for Linear Programming Based on a Kernel Function

A Full-Newton Step Infeasible Interior-Point Algorithm for Linear Programming Based on a Kernel... This paper proposes an infeasible interior-point algorithm with full-Newton step for linear programming, which is an extension of the work of Roos (SIAM J. Optim. 16(4):1110–1136, 2006 ). The main iteration of the algorithm consists of a feasibility step and several centrality steps. We introduce a kernel function in the algorithm to induce the feasibility step. For parameter p ∈(0,1), the polynomial complexity can be proved and the result coincides with the best result for infeasible interior-point methods, that is, O ( n log n / ε ). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

A Full-Newton Step Infeasible Interior-Point Algorithm for Linear Programming Based on a Kernel Function

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Publisher
Springer-Verlag
Copyright
Copyright © 2009 by Springer Science+Business Media, LLC
Subject
Mathematics; Numerical and Computational Methods ; Mathematical Methods in Physics; Mathematical and Computational Physics; Systems Theory, Control; Calculus of Variations and Optimal Control; Optimization
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/s00245-009-9069-x
Publisher site
See Article on Publisher Site

Abstract

This paper proposes an infeasible interior-point algorithm with full-Newton step for linear programming, which is an extension of the work of Roos (SIAM J. Optim. 16(4):1110–1136, 2006 ). The main iteration of the algorithm consists of a feasibility step and several centrality steps. We introduce a kernel function in the algorithm to induce the feasibility step. For parameter p ∈(0,1), the polynomial complexity can be proved and the result coincides with the best result for infeasible interior-point methods, that is, O ( n log n / ε ).

Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Oct 1, 2009

References

  • An infeasible interior-point algorithm with full-Newton step for linear optimization
    Liu, Z.; Sun, W.

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