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).
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.
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.
Date and Time Tuesday 4 October 2016, 11:00am-12:00pm.
Speaker: Dr Vera Roshchina, RMIT University
Date and Time: Tuesday 2 August 2016, 11:00am
Title: Subdifferentials of structured functions
I will talk about geometric construction of Fréchet and limiting subdifferentials for finite minima of functions subdifferentiable in the sense of Demyanov-Rubinov. Such functions have convex directional derivatives and under additional assumptions their subdifferentials preserve enough directional information to make such construction possible. For instance, approximate convex functions introduced by Huynh Van Ngai, Dinh The Luc and Michel Théra satisfy such assumptions.
These results are in the same spirit as the classic expressions for the Clarke subdifferential in terms of quasidifferentials originally developed by Demyanov and Rubinov.
The talk will be based on some old papers and recent joint work with Tian Sang (RMIT University).