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.
Anna Weigandt. Kaitlyn Tuthill. Shafiu Jibrin. "Constraint Consensus Methods for Finding Interior Feasible Points in Second-Order Cones." J. Appl. Math. 2010 1 - 19, 2010. https://doi.org/10.1155/2010/307209