Mitch is a final-year student in the Bachelor of Science at the University of New England and will commence his honours in mathematics in 2019. He has broad mathematical interests, including optimisation, complex analysis, discrete mathematics, and machine learning. Mitch’s hobbies include reading and training Brazilian Jiu-Jitsu. As he is intending to pursue a PhD, the AMSI Vacation Research Scholarship will be a good introduction to mathematical research.
Convex Hulls of Graphs of Structured Bilinear Functions
Convex envelopes of non-convex functions play an important role in global optimisation. The project aims to find minimal characterisations of convex hulls of graphs of bilinear functions. The structure of a bilinear function can be described in terms of a graph with vertices corresponding to the variables and edges corresponding to the product terms. A new geometric method that has been developed last year can in special cases characterise the convex hull. In particular, the convex hull is known when the associated graph is the 5-wheel, and it is conjectured that this result can be extended to the n-wheel for arbitrary n. The goal of this project is to make progress towards proving this conjecture, or to construct a counterexample. This may give insight into how far this method can be pushed, and potentially lead to minimal convexifications for large classes of functions.