Parallel projected variable metric algorithms for unconstrained optimization

The parallel variable metric optimization algorithms of Straeter (1973) and van Laarhoven (1985) are reviewed, and the possible drawbacks of the algorithms are noted. By including Davidon (1975) projections in the variable metric updating, researchers can generalize Straeter's algorithm to a family of parallel projected variable metric algorithms which do not suffer the above drawbacks and which retain quadratic termination. Finally researchers consider the numerical performance of one member of the family on several standard example problems and illustrate how the choice of the displacement vectors affects the performance of the algorithm.