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.