Extensions of Hildreth’s Row-Action Method for Quadratic Programming

An extended version of Hildreth?s iterative quadratic programming algorithm is presented, geometrically interpreted, and proved to produce a sequence of iterates that (i) converges to the solution, and (ii) has an important intermediate optimality property. This extended Hildreth algorithm is cast into a new form which more pronouncedly brings out its primal-dual nature. The application of the algorithm may be governed by an index sequence which is more general than a cyclic sequence, namely, by an almost cyclic control, and a sequence of relaxation parameters is incorporated without ruining convergence. The algorithm is a row-action method which is particularly suitable for handling large (or huge) and sparse systems.