An O(n 2) Active Set Algorithm for Solving Two Related Box Constrained Parametric Quadratic Programs - Gómez, Manuel A. (Numerical algorithms, 2001)
Recently, O(n2) active set methods have been presented for minimizing the parametric quadratic functions (1/2)x′Dx−a′x+λ|γ′x−c| and (1/2)x′Dx−a′x+(λ/2)(γ′x−c)2, respectively, subject to l≤x≤b, for all nonnegative values of the parameter λ. Here, D is a positive diagonal n×n matrix, γ and a are arbitrary n-vectors, c is an arbitrary scalar; l and b are arbitrary n-vectors such that l≤b. In this paper, we show that each one of these algorithms may be used to simultaneously solve both parametric programs withno additional computational cost.