Time: 9Am, Wednesday 31 January, 2024

Venue: Room 612, building A6

Abstract: This presentation examines two fundamental aspects of variational analysis: proto-differentiability in monotone inclusions and the graphical convergence of maximally monotone operators in Hilbert spaces. The first part explores the sensitivity of parametrized variational inclusions with maximal monotone operators, focusing on the differentiability of solutions and the proto-derivative of the resolvent operator. This leads to insights into the differentiability of primal and dual solutions in primal-dual composite monotone inclusions. The second part investigates whether maximally monotone properties persist in the limit operator under graphical convergence, specifically under Painlevé-Kuratowski convergence and bounded Hausdorff topology. This study contributes to the theoretical understanding in variational analysis and optimization and also offers practical insights in the sensitivity analysis of monotone variational inclusions.

The presentation is based on the following papers:

1. S. Adly, R.T. Rockafellar. Sensitivity analysis of monotone inclusions via the proto-differentiability of the resolvent operator. Math. Prog. Ser. B. 2021.
2. S. Adly, H. Attouch, R.T. Rockafellar. Preserving, or not, the maximally monotone property by the graph-convergence. Journal of Convex Analysis. 2023.