Thesis Defence: Using Complex Step Numerical Differentiation in the Broyden-Fletcher-Goldfard-Shanno Algorithm

Jinghong (Joe) Chen, supervised by Dr. Warren Hare, will defend their thesis titled “Using Complex Step Numerical Differentiation in the Broyden-Fletcher-Goldfard-Shanno Algorithm” in partial fulfillment of the requirements for the degree of Master of Science in Computer Science.

An abstract for Jinghong’s thesis is included below.

Defence are open to all members of the campus community as well as the general public. Registration is not required for in-person defences.

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ABSTRACT

We conduct a study on an alternative method of Derivative-Free optimization (DFO). It is a method by applying numerical differentiation techniques to the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm on unconstrained optimization. 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 method. 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, approximationbased-BFGS methods archive high level accuracy relative to the original BFGS method. Among different numerical differentiation techniques, the approximation-based-BFGS method with complex-step acheives outstanding and stable performance in accuracy.