A Feasible Active Set Method for Strictly Convex Quadratic Problems with Simple Bounds
提出一种原始-对偶积极集方法求解带边界约束的二次问题，通过迭代调整积极集直至获得可行解，适用于严格凸二次问题，理论保证有限步收敛且实际表现良好。
A primal-dual active set method for quadratic problems with bound constraints is presented which extends the infeasible active set approach of Kunisch and Rendl [SIAM J. Optim., 14 (2003), pp. 35--52]. Based on a guess of the active set, a primal-dual pair ($x$,$\alpha$) is computed that satisfies stationarity and the complementary condition. If $x$ is not feasible, the variables connected to the infeasibilities are added to the active set, and a new primal-dual pair ($x$,$\alpha$) is computed. This process is iterated until a primal feasible solution is generated. Then a new active set is determined based on the feasibility information of the dual variable $\alpha$. Strict convexity of the quadratic problem is sufficient for the algorithm to stop after a finite number of steps with an optimal solution. Computational experience indicates that this approach also performs well in practice.