Recovering optimal solutions via SOC-SDP relaxation of trust region subproblem with nonintersecting linear constraints
Jinyu Dai, Shu‐Cherng Fang, Wenxun Xing · Journal of Industrial and Management Optimization · 2018
In this paper, we study an extended trust region subproblem (eTRS) in which the unit ball intersects with $m$ linear inequality constraints. In the literature, Burer et al. proved that an SOC-SDP relaxation (SOCSDPr) of eTRS is exact, under the condition that the nonredundant constraints do not intersect each other in the unit ball. Furthermore, Yuan et al. gave a necessary and sufficient condition for the corresponding SOCSDPr to be a tight relaxation when $m = 2$. However, there lacks a recovering algorithm to generate an optimal solution of eTRS from an optimal solution $X^*$ of SOCSDPr when rank $(X^*)≥ 2$ and $m≥ 3$. This paper provides such a recovering algorithm to complement those known works.