Semidefinite programming (SDP) problems typically utilize the constraint that X-xx' is PSD to obtain a convex relaxation of the condition X=xx', where x is an n-vector. In this paper we consider a new hyperplane branching method for SDP based on using an eigenvector of X-xx'. This branching technique is related to previous work of Saxeena, Bonami and Lee (2010) who used such an eigenvector to derive a disjunctive cut. We obtain excellent computational results applying the new branching technique to difficult instances of the two-trust-region subproblem.
Dept. of Business Analytics, University of Iowa, February 2022