Resolving degeneracy in quadratic programming

A technique for the resolution of degeneracy in an Active Set Method for Quadratic Programming is described. The approach generalises Fletcher’s method which applies to the LP case. The method is described in terms of an LCP tableau, which is seen to provide useful insights. It is shown that the degeneracy procedure only needs to operate when the degenerate constraints are linearly dependent on those in the active set. No significant overheads are incurred by the degeneracy procedure. It is readily implemented in a null space format, and no complications in the matrix algebra are introduced. The guarantees of termination provided by Fletcher’s LP method extending in particular to the case where round-off error is present, are preserved in the QP case. It is argued that the technique gives stronger guarantees than are available with other popular methods such as Wolfe’s method or the method of Goldfarb and Idnani.