An Active-Set Method for Second-Order Conic-Constrained Quadratic Programming
提出一种两阶段方法求解凸二次目标受二阶锥约束的优化问题，第一阶段用投影梯度法快速识别积极锥集，第二阶段用牛顿法快速收敛，实验表明比专用锥优化求解器更高效、比通用非线性规划求解器更稳健。
We consider the minimization of a convex quadratic objective subject to second-order cone constraints. This problem generalizes the well-studied bound-constrained quadratic programming (QP) problem. We propose a new two-phase method: in the first phase a projected-gradient method is used to quickly identify the active set of cones, and in the second-phase Newton's method is applied to rapidly converge given the subsystem of active cones. Computational experiments confirm that the conically constrained QP is solved more efficiently by our method than by a specialized conic optimization solver and more robustly than by general nonlinear programming solvers.