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Journal of Applied Mathematics
Volume 2010, Article ID 307209, 19 pages
Research Article

Constraint Consensus Methods for Finding Interior Feasible Points in Second-Order Cones

1Department of Mathematics, Illinois State University, Normal, IL 61790-4520, USA
2Department of Mathematics, Saint Michael's College, Colchester, VT 05439, USA
3Department of Mathematics and Statistics, Northern Arizona University, Flagstaff, AZ 86011-5717, USA

Received 29 August 2010; Revised 17 November 2010; Accepted 17 December 2010

Academic Editor: Tak-Wah Lam

Copyright © 2010 Anna Weigandt et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Optimization problems with second-order cone constraints (SOCs) can be solved efficiently by interior point methods. In order for some of these methods to get started or to converge faster, it is important to have an initial feasible point or near-feasible point. In this paper, we study and apply Chinneck's Original constraint consensus method and DBmax constraint consensus method to find near-feasible points for systems of SOCs. We also develop and implement a new backtracking-like line search technique on these methods that attempts to increase the length of the consensus vector, at each iteration, with the goal of finding interior feasible points. Our numerical results indicate that the new methods are effective in finding interior feasible points for SOCs.