Recovering optimal solutions via SOC-SDP relaxation of trust region subproblem with nonintersecting linear constraints

Jinyu Dai, Shu-Cherng Fang, Wenxun Xing
2017 Journal of Industrial and Management Optimization  
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
more » ... e 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.
doi:10.3934/jimo.2018117 fatcat:vkxoltbcpjcifakdxrd3k5kd3u