Range-Space Method for Quadratic Programming Problems with Bounds and General Constraints

摘要

This report concerns quadratic programming problems which include simple bounds on all the variables as well as general linear constraints. Range-space methods for convex quadratic programming improve in efficiency as the number of constraints active at the solution decreases. This paper describes how the weighted Gram-Schmidt range-space method may be implemented to exploit the special structure of bound constraints. The results of this adaptation are (1) the method retains efficiency when the number of general constraints active at the solution is small; and (2) the efficiency of the method improves as the number of active bound constraints increases.