Elementary Sources of Concurrency in a Standard Quasi-Newton Unconstrained Nonlinear Optimization Algorithm.

摘要

Neglecting scaling and stopping features, a standard quasi-Newton unconstrained nonlinear optimization algorithm has three main aspects--the Newton step, modifications to this step to ensure global convergence, and a possible secant approximation to the Hessian. We will discuss these aspects and the concurrencies associated with them. Before going into details, however, we make the general observation that there are two main sources of concurrency in the algorithms under consideration--function evaluations and linear algebra. If the function to be minimized and its derivatives are expensive to evaluate, we can expect good speedups from concurrent evaluations. If, on the other hand, function evaluation costs are relatively low, and the number of parameters (over which we are minimizing) is large, the greatest speedups will be obtained via concurrent linear algebra routines. We provide a brief introduction to sources of concurrency that are available at a higher level of sophistication, and that are currently under study. 11 refs. (ERA citation 13:058336)