A limited memory interior points technique for nonlinear optimization

We propose the use of Limited memory representation of Quasi-Newton matrices in an interior points algorithm for nonlinear optimization with inequality constraints. This algorithm is based on the iterative solution of the non-linear system generated by Karush-Kuhn-Tucker first order optimality conditions, being the exact Hessian replaced by its BFGS approximation. Good theoretical results have been already obtained on this method, that proved to be strong and efficient when applied to optimization problems in mechanics. However, as the Quasi-Newton matrix is full, a large amount of memory can be required. The present algorithm seems to be a very suitable approach for large-scale problems once we avoid the storage of the Quasi-Newton matrix and only two linear systems, having each one the dimension of the number of constraints, must be solved at each iteration.