A primal-dual active set method for quadratic problems with bound constraints is presented which extends the infeasible active set approach of [K. Kunisch and F. Rendl. An infeasible active set method for convex problems with simple bounds. SIAM Journal on Optimization, 14(1):35-52, 2003]. Based on a guess of the active set, a primal-dual pair (x,α) 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,α) 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 α. 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.
Citation
SIAM Journal on Optimization, 25(3):1633–1659, 2015.
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View A feasible active set method for strictly convex problems with simple bounds