A relaxed-certificate facial reduction algorithm based on subspace intersection

A “facial reduction”-like regularization algorithm is established for general conic optimization problems by relaxing requirements on the reduction certificates. This yields a rapid subspace reduction algorithm challenged only by representational issues of the regularized cone. A condition for practical usage is analyzed and shown to always be satisfied for single second-order cone optimization problems. Should the condition fail on some other class of instances, only partial regularization is achieved based on the success of the individual subspace intersection.