Maths Seminar Series: Hoa Bui Tui, Federation University – On Fréchet Subdifferential Calculus with Applications to Nonsmooth and Nonconvex Optimization

Most of optimization problems and many fundamental objects frequently appearing in the framework of variational analysis are non-smooth and non-convex. When dealing with non-smoothness, generalized subdifferential calculus becomes inevitably crucial. In this talk, we brie􏰙ly discuss Fréchet subdifferential calculus for general extended real-valued functions on Asplund spaces.

We will discuss in detail two different approaches. The 􏰙irst approach is to consider a broader than convex class of functions, so-called generalised convex functions, which still possess certain important properties of convex functions needed in optimisation. The second approach is to develop a very general theory for extended real-valued functions. Both directions have their advantages and disadvantages and both are important for non-convex optimization and analysis.

At the end of the talk, we will also discuss some results in convergence analysis with some open prob- lems for future study.

Hoa Bui is a PhDs student in Mathematics at Federation University Australia and a member of CIAO, working in variational analysis and non-smooth optimisation.

Hoa is in the third year of her PhD, commenced in December 2016.