REPRESENTATIONS OF QUASI-NEWTON MATRICES AND THEIR USE IN LIMITED MEMORY METHODS

We derive compact representations of BFGS and symmetric rank-one matri ces for optimization. These representations allow us to efficiently im plement limited memory methods for large constrained optimization prob lems. In particular, we discuss how to compute projections of limited memory matrices onto subspaces. We also present a compact representati on of the matrices generated by Broyden's update for solving systems o f nonlinear equations.