On the Location of Directions of Infinite Descent for Nonlinear Programming Algorithms

There is much current interest in general equality constrained quadratic programming problems, both for their own sake and for their applicability to active set methods for nonlinear programming. In the former case, typically, the issues are existence of solutions and their determination. In the latter instance, nonexistence of solutions gives rise to directions of infinite descent. Such directions may subsequently be used to determine a more desirable active set.The generalised Cholesky decomposition of relevant matrices enables us to answer the question of existence and to determine directions of infinite descent (when applicable) in an efficient and stable manner.The methods examined are related to implementations that are suitable for null-space, range-space and Lagrangian methods.