I am giving a talk at Monash ACM seminar series on Friday, 10th of March, 2-3pm in Room 340.
Title: Open problems in convex geometry
Abstract: A convex model is the second best thing after a closed-form solution. Convex optimisation problems are often highly tractable, with a variety of numerical methods producing reliable approximations or exact solutions. The choice of the algorithms is vast, and includes general techniques such as subgradient descent or alternating projections, as well as highly specialised simplex and interior point methods. The major factors in the choice of the particular technique are the structure of the problem and the trade-offs between the resources available, the desired accuracy and the reliability of solutions.