26 Apr

Two applications of lexicographic differentiation

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).

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10 Mar

Open problems in convex geometry

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.

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13 Dec

Talk at the Workshop on Variational Analysis with Applications

Title: Outer limits of subdifferentials for min-max type functions
Date and Place: Workshop on Variational Analysis with Applications, 13–14 December 2016, PolyU (Hong Kong)
Abstract: Outer limits of subdifferentials is a limiting construction that can be used to estimate the error bound modulus. We present some new result related to the evaluation of such limiting subdifferentials for max-type and min-max functions.

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10 Oct

Workshop on Metric Bounds and Transversality (WoMBaT 2016)

wombat

The meeting will be held in Melbourne (RMIT City Campus, room 8.9.66) on 24–25 November.

The topics of the workshop include error bounds, metric (sub) regularity, Aubin property and calmness, transversality of collections of sets, subdifferential characterisations and applications of these properties to estimating the convergence of fundamental optimisation algorithms. Our keynote is Professor Marco Lopez from the University of Alicante, Spain, who is visiting Australia in November.

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