An Inverse-Basis Method for Beale's Quadratic Programming Algorithm

This paper presents a version of Beale's Quadratic Programming Algorithm [Beale, E. M. L. 1959. On quadratic programming. Naval Res. Logist. Quart.6 227–243; Beale, E. M. L. 1967. Numerical methods. J. Abadie, ed. Nonlinear Programming. Amsterdam.] for solving a problem of maximising a quadratic function under linear constraints. The modification discussed here makes it possible to retain the “inverse basis” tableau which has to be augmented by additional constraints to be called “auxiliary.” The algorithm has been successfully tested on a computer.