"Representations of Quasi-Newton Matrices and their use in Limited Memory Methods"
R. Byrd, J. Nocedal, R. Schnabel.
Mathematical Programming, Vol. 63, No. 4, pp. 129-156 (1994)
We derive compact representations of BFGS and symmetric rank-one matrices for optimization. These representations allow us to efficiently implement limited memory methods for large constrained optimization problems. In particular, we discuss how to compute projections of limited memory matrices onto subspaces. We also present a compact representation of the matrices generated by Broyden's update for solving systems of nonlinear equations.