On modified factorizations for large-scale linearly constrained optimization

We consider the algebraic issues concerning the solution of general, large- scale, linearly constrained nonlinear optimization problems. Particular att ention is given to suitable methods for solving the linear systems that occ ur at each iteration of such methods. The main issue addressed is how to en sure that a quadratic model of the objective function is positive definite in the null-space of the constraints while neither adversely affecting the convergence of Newton's method nor incurring a significant computational ov erhead. Numerical evidence to support the theoretical developments is provi ded.