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Solving Limited-Memory BFGS Systems With Generalized Diagonal Updates

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Executive Summary

Limited memory (L-BFGS) quasi-Newton methods are powerful tools within the field of optimization for solving problems when second derivative information is not available or computing the second derivative is too computationally expensive. In addition, L-BFGS matrices can be used to precondition iterative methods for solving large linear systems of equations. For both L-BFGS methods and preconditioning schemes, being able to solve linear systems with L-BFGS matrices are of utmost importance. While there is a well-known two-loop recursion for solving linear systems with L-BFGS matrices, little is known about solving systems involving matrix modifications of L-BFGS matrices.

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