Daniel Molent is a student from RMIT University undertaking optimisation research. After living in coastal Victoria, Daniel moved to Melbourne after finishing his secondary education to pursue his interest in mathematics. He recently completed his second year of a Bachelor of Analytics (Honours) and a unit in Nonlinear Optimisation. During the course, Daniel developed a passion for optimisation, deciding to explore the area of study further through research. When he is not studying mathematics, Daniel enjoys reading fictional novels and spending time at coffee shops with his friends.
Experiments with Trust Regions and the BFGS Method in Nonsmooth Optimisation
In recent years researchers have noticed that the classical BFGS descent method actually converges for some nonsmooth (nondifferentiable) optimisation problems if one uses subgradients instead if derivatives and one tunes the line search correctly. This project will consider how the trust region philosophy might be turned to the use of BFGS steps in nonsmooth optimisation. Trust regions are an alternative to doing a line search and are essentially based on an approach that compares the predicted descent to what actually is obtained in a step in order to improve a local “model” of the function being minimised. The step direction and length is derived from this local model. A number of numerical experiments will be trialled, and we will also try and construct illustrative 2-dimensional examples that can be plotted (or animated) to illustrate its behaviour in Matlab or using GeoGebra. We hope to gain some insight into this class of algorithm and how they can be better tuned to effect better behaviour. We will also compare this with the BFGS with the modified line search given in the literature to compare effectiveness.