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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Talk at Federation University Australia

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).

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