主 题：Calculus rules for subdifferentials （次微分的计算法则）
主讲人：皇家墨尔本理工大学 Vera Roshchina博士
主持人：经济数学学院 张文燕 副教授
Dr. Vera Roshchina is a DECRA Research Fellow at the School of Science, RMIT University. She works on finite dimensional optimisation problems, focussing on the geometry of underlying objects. This includes subdifferential calculus in finite dimensions and the study of facial structure of convex sets. Vera received her Ph.D. in applied mathematics from the City University of Hong Kong in 2009. Prior to joining RMIT University in 2015 she held postdoctoral positions at University of Evora (Portugal), Federation University Australia and The University of Melbourne. She has published around 30 papers in international journals in the areas of subdifferential calculus, real complexity and dynamical systems.
Subdifferentials generalise the notion of derivative for functions which are nonsmooth. There are different ways to define such generalisations. 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.