# Colloquium abstracts

**M. Vanninathan**

IIT, Mumbai

March 1, 2018

**Optimal Design Problems and Beyond**: It is well-known that the study of classical problems of Calculus of Variations usually requires structural conditions such as compactness, continuity, and convexity. This talk is about a class of optimization problems that arise in engineering, and which do not possess the above qualities. Analysis and computations in such problems become then non-trivial issues. One idea to overcome this difficulty is to relax the problem;but the relaxation for the class of problems under consideration involves the description of the G-closure set (and its extension) which are, in general, open problems. The implementation of these ideas requires new notions of convergence and new tools of analysis. The goal of the talk is to survey this material.