A survey of quasi‐Newton methods with reduced storage
Manolis Papadrakakis, George Pantazopoulos · International Journal for Numerical Methods in Engineering · 1993
Abstract A family of non‐linear solution methods is investigated based on limited‐memory quasi‐Newton updates. Depending upon the number of updates and the updating formula, a number of solution schemes may be constructed such as the conjugate‐ and secant‐Newton methods, the conventional and modified Newton‐Raphson methods and a variety of quasi‐Newton updates. Under the proposed implementation, the preconditioned truncated Lanczos method is used for the solution of the linearized problem in each non‐linear iteration. The complete factorization of the stiffness matrix is avoided and large‐scale problems can be solved efficiently both in terms of computing time and storage. The non‐linear iterative scheme is properly modified to account for loading variation inside the increment in order to be able to trace post‐critical equilibrium paths.