Article ID: | iaor1988699 |
Country: | Switzerland |
Volume: | 14 |
Start Page Number: | 167 |
End Page Number: | 193 |
Publication Date: | Dec 1988 |
Journal: | Annals of Operations Research |
Authors: | Byrd Richard H., Schnabel Robert B., Shultz Gerald A. |
Keywords: | parallel processing |
This paper presents a new class of methods for solving unconstrained optimization problems on parallel computers. The methods are intended to solve small to moderate dimensional problems where function and derivative evaluation is the dominant cost. They utilize multiple processors to evaluate the function, (finite difference) gradient, and a portion of the finite difference Hessian simultaneously at each iterate. The authors introduce three types of new methods, which all utilize the new finite difference Hessian information in forming the new Hessian approximation at each iteration; they differ in whether and how they utilize the standard secant information from the current step as well. They present theoretical analyses of the rate of convergence of several of these methods. The authors also present computational results which illustrate their performance on parallel computers when function evaluation is expensive.