UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Using complex step numerical differentiation in the Broyden-Fletcher-Goldfard-Shanno algorithm Chen, Jinghong

Abstract

We conduct a study on an alternative method to Derivative-Free Optimization (DFO). It is a method by applying numerical differentiation techniques to the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm. We apply different gradient approximation strategies on the BFGS, particularly a complex-step method to the gradient approximation. We conduct an experiment to test the feasibility of the approximation-based-BFGS methods. The experiment also explores the efficiency and reliability of BFGS algorithm with different strategies and different settings. Results find that the approximation-based-BFGS method is feasible alternative to DFO. With appropriate parameter settings, approximation-based-BFGS methods achieve high level accuracy relative to the original BFGS method. Among different numerical differentiation techniques, the approximation-based-BFGS method with complex-step achieves outstanding and stable performance in accuracy.

Item Media

Item Citations and Data

Rights

Attribution-NonCommercial-NoDerivatives 4.0 International