An Efficient Single-Parameter Scaling Memoryless Broyden-Fletcher-Goldfarb-Shanno Algorithm for Solving Large Scale Unconstrained Optimization Problems

In this paper, a new spectral scaling memoryless Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm is developed for solving large scale unconstrained optimization problems, where the scaling parameter is chosen so as to minimize all the eigenvalues of search direction matrices. The search directions in this algorithm are proved to satisfy the approximate Dai-Liao conjugate condition. With this advantage of the search directions, a scaling memoryless BFGS update formula is constructed and an algorithm is developed by incorporating acceleration strategy of line search and restart criterion. Under mild assumptions, global convergence of the algorithm is proved. Numerical tests demonstrate that the developed algorithm is more robust and efficient in solving large scale benchmark test problems than the similar ones in the literature.