A parallel unconstrained quasi-Newton algorithm and its performance on a local memory parallel computer

The paper reviews the parallel quasi-Newton optimisation algorithms of Straeter and van Laarhoven and points out the possible drawbacks of these algorithms. By including Davidon projections in the variable metric updating Straeter’s algorithm can be generalised to a family of parallel projected quasi-Newton algorithms which do not suffer the above drawbacks and which retain quadratic termination. The paper considers the implementation of this parallel algorithm on the Intel iPSC/2 Hypercube. Finally it compares, on several standard example problems, the numerical performance of this new algorithm with Straeter’s parallel algorithm and with a sequential quasi-Newton (BFGS) algorithm.