Some Preconditioned Conjugate Gradient Algorithms for the Solution of Equality Constrained Quadratic Programming Problems

In this paper we consider the application of the preconditioned conjugate gradient (PCG) method to the solution of equality constrained quadratic programming problems. In particular, we consider three different PCG algorithms and two indefinite preconditioners. A special attention is given to the choice of the factorization method for the preconditioner. The numerical experiments show a comparison of the effectiveness of the proposed variants. Furthermore, we show the behaviour of the PCG method for the solution of the inner subproblem arising at each step of an interior point algorithm for the solution of non linear programming problems.