TY - JOUR A1 - Qu, Zheng A1 - Zeng, Tianyou A1 - Lou, Yuchen T1 - Globally solving concave quadratic programs via doubly nonnegative relaxation T2 - Mathematical Programming Computation N2 - We consider the problem of maximizing a convex quadratic function over a bounded polyhedral set. We design a new framework based on SDP relaxations and cutting plane methods for solving the associated reference value problem. The major novelty is a new way to generate valid cuts through the doubly nonnegative (DNN) relaxation. We establish various theoretical properties of the DNN relaxation, including its equiv- alence with the Shor relaxation of an equivalent quadratically constrained problem, the strong duality, and the generation of valid cuts from an approximate solution of the DNN relaxation returned by an arbitrary SDP solver. Computational results on both real and synthetic data demonstrate the efficiency of the proposed method and its ability to solve high-dimensional problems with dense data. In particular, our new algorithm successfully solves in 3 days the reference value problem arising from com- putational biology for a dataset containing more than 300,000 instances of dimension 78. In contrast, CPLEX or Gurobi is estimated to require years of computational time for the same dataset on the same computing platform. Y1 - 2025 UR - https://opus4.kobv.de/opus4-mpc/frontdoor/index/index/docId/298 SN - 1867-2949 VL - 17 IS - 3 SP - 451 EP - 503 PB - Springer Science and Business Media LLC ER -