New results on eliminating the duality gap of the second-order-cone reformulation for extended trust-region subproblem with two intersecting cuts - Wang, Meiling (Comptes Rendus. Mathématique)
In this paper, we consider the nonconvex extended trust-region subproblem with two intersecting linear inequality constraints, $(ETR_2)$, and use a sequence of semi-definite programming (SDP) problems with second-order-cone(SOC) constraints to eliminate the duality gap of the SOC reformulation for $(ETR_2)$. We first narrow the duality gap of the SOC reformulation by adding a new appropriate SOC constraint, and a sufficient condition is presented to characterize when the new SOC constraint is valid. Then we establish an iterative algorithm and the results of numerical experiments show that the iterative algorithm works efficiently in eliminating the SDPR-SOCR gap of $(ETR_2)$.