Self-Scaling Parallel Quasi-Newton Methods

In this paper, a new class of self-scaling quasi-Newton(SSQN) updates for solving unconstrained nonlinear optimization problems(UNOPs) is proposed. It is shown that many existing QN updates can be considered as special cases of the new family. Parallel SSQN algorithms based on this class of class of updates are studied. In comparison to standard serial QN methods, proposed parallel SSQN(SSPQN) algorithms show signi cant improvement in the total number of iterations and function/gradient evaluations required in solving a wide range of test problems. In fact, the average speedup factors by the new SSPQN algorithms over the conventional BFGS method and E04DGE in NAG library are 3:22=3:13 and 2:80=3:09 , respectively(in terms of total number of iterations and total number of function/gradient evaluations required). For some test problems, the speedup factor gained by the new algorithms can be as high as 25/25 over BFGS and 20/25 over E04DGE , both in terms of total number of iterations and function/gradient evaluations.