In this talk, we discuss various aspects of twice epi-differentiablity of extended-real-valued functions and its remarkable applications in parametric optimization, second-order variational analysis, and local convergence analysis of the augmented Lagrangian method. We begin with presenting the history of this concept and then proceeding with its evolution in the last three decades.

Twice Epi-Differentiability : Past, Present, and Future

In this talk, we discuss various aspects of twice epi-differentiablity of extended-real-valued functions and its remarkable applications in parametric optimization, second-order variational analysis, and local convergence analysis of the augmented  Lagrangian method. We begin with presenting the history of this concept and then proceeding with its evolution in the last three decades. In particular, we demonstrate that this property often holds for various classes of functions, important for applications to optimization problems. Finally, we discuss how a generalization of this concept leads us to achieve a characterization of continuous differentiability of the projection mapping for a large class of sets. This talk is based on joint works with Nguyen T. V. Hang, Ashkan Mohammadi, and Boris Mordukhovich. 

Berif Bio

Ebrahim Sarabi received his Ph.D. from the department of mathematics at Wayne State University in 2016. He joined Miami University in August 2016 as an assistant professor and was promoted to an associate professor in 2022. His research has been focused on second-order generalized differentiation and its applications into parametric optimization and numerical algorithms. He serves as an associated editor for the Journal of Nonsmooth Analysis and Optimization and Journal of Optimization Theory and Applications

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