Parallel Algorithms for Large-scale Nonlinear Optimization

Multi-step, multi-directional parallel variable metric (PVM) methods for unconstrained optimization problems are presented in this paper. These algorithms generate several VM directions at each iteration, dierent line search and scaling strategies are then applied in parallel along each search direction. In comparison to some serial VM methods, computational results show that a reduction of 200% or more in terms of number of iterations and function/gradient evaluations respectively could be achieved by the new parallel algorithm over a wide range of 63 test problems. In particular, when the complexity, or the size of the problem increases, greater savings could be achieved by the proposed parallel algorithm. In fact, the speedup factors gained by our PVM algorithms could be as high as 28 times for some test problems.