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

[摘要] Optimization problems with second-order cone constraints (SOCs) can be solved efficientlyby interior point methods. In order for some of these methods to get started orto converge faster, it is important to have an initial feasible point or near-feasible point. In this paper, we study and apply Chinneck'sOriginalconstraint consensus method andDBmaxconstraint consensus method to find near-feasible points for systems of SOCs. We also develop and implement a new backtracking-like line search technique on thesemethods 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 thenew methods are effective in finding interior feasible points for SOCs.

[学科分类] 应用数学