Block truncated-Newton methods for parallel optimization

Truncated-Newton methods are a class of optimization methods suitable for large scale problems. At each iteration, a search direction is obtained by approximately solving the Newton equations using an iterative method. In this way, matrix costs and second-derivative calculations are avoided, hence removing the major drawbacks of Newton’s method. In this form, the algorithms are well-suited for vectorization. Further improvements in performance are sought by using block iterative methods for computing the search direction. In particular, conjugate-gradient-type methods are considered. Computational experience on a hypercube computer is reported, indicating that on some problems the improvements in performance can be better than that attributable to parallelism alone.