2020/12/18 by Huu-Quang Nguyen, Nguyen, Huu-Quang, Ruey-Lin Sheu +1
Computer Science · Engineering · Mathematics · #90C20 #90C22 #90C26 #Advanced Control Systems Optimization #Advanced Optimization Algorithms Research #F.2 #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis
paper · pdf · doi:10.48550/arxiv.2012.10299
openalex publication_date 2020/12/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study a special class of non-convex quadratic programs subject to two (possibly indefinite) quadratic constraints when the level sets of the constraint functions are \it not arranged \it alternatively. It is shown in the paper that this class of problems admit strong duality following a tight SDP relaxation, without assuming primal or dual Slater conditions. Our results cover Ye and Zhang's development in 2003 and the generalized trust region subproblems (GTRS) as special cases. Through the novel geometric view and some simple examples, we can explain why the problem becomes very hard when the level sets of the constraints are indeed arranged alternatively.