New low storage VM-algorithm for constrained optimization

In this paper a new low-storage VM-algorithm for constrained optimization is investigated both theoretically and experimentally. The new algorithm is based on both the well-known Fletcher's low storage algorithm which generates columns Z spanned on the gradient vectors g1, g2, ... gn and the idea of both Buckley and LeNir of combined variable storage-conjugate gradient method. The well-known SUMT algorithm is adapted to implement the new idea. The new algorithm is very robust compared with the standard low-storage Fletcher algorithm and the standard SUMT algorithm which was designed for solving constrained problems, of the numerical results of application very promising.