An Algorithm for the Solution of the Parametric Quadratic Programming Problem

We present an ”active set” algorithm for the solution of the convex (but not necessarily strictly convex) parametric quadratic programming problem. The optimal solution and associated multipliers are obtained as piece-wise linear functions of the parameter. At the end of each interval, the active set is changed by either adding, deleting, or exchanging a constraint. The method terminates when either the optimal solution has been obtained for all values of the parameter, or, a further increase in the parameter results in either the feasible region being null or the objective function being unbounded from below. The method used to solve the linear equations associated with a particular active set is left unspecified. The parametric algorithm can thus be implemented using the linear equation solving method of any active set quadratic programming algorithm.