The talk is based on the joint paper with Tian Sang and David Yost.
Continue reading "Talk at SIAM Conference on Optimisation"
Lexicographic differentiation was introduced by Yurii Nesterov in 1987. A recent and more accessible overview is given in his Mathematical Programming paper. At the CIAO workshop on 27 April I talk about lexicographic differentiation and mention two applications: the construction of directed subdifferential and geometric conditions for facial dual completeness of closed convex cones.
The function shown in the Mathematica rendering is lexicographically smooth, but is neither quasidifferentiable nor tame. The idea of this example was suggested by Jeffrey Pang (NUS).
Albrecht Dürer dedicated a nontrivial part of his career to laying out the geometric foundations of drawing and perspective. His five centuries old work is available online via Google books. Continue reading "Dürer's conjecture"
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.
Continue reading "Open problems in convex geometry"
Date and time: 3 November 2016, 10:00am
Location: Hangzhou Dianzi University
Date and time: 7 November 2016, 10:00am
Location: Southwest Jiaotong University, more info
Title: Facial structure of convex sets
Continue reading "Talk on facial structure in Hangzhou and Chengdu"
Convexity has seemingly little to do with fractals, however convex sets with fractal facial structure are not hard to imagine. Continue reading "Fractal convex sets"