Continuous Optimization from Variational Analysis' viewpoint
Ashkan Mohammadi - Postdoctoral Researcher, University of Minnesota
Sun, 12-Sep-2021 / 15:30 / Link:
Video Slides Poster
In this talk, we briefly introduce variational analysis as the complement of the (classic) mathematical analysis. Then, we show how variational analysis can build a complete theory for continuous optimization where classical analysis cannot do the same task!
This talk is devoted to the first- and second-order variational analysis. The key is generalized differentiation leading us to the first- and second-order optimality conditions. In the first-order variational analysis, we develop exact first-order calculus via both subderivative and subdifferential. The latter is used to drive first-order optimality conditions for a general constrained optimization. We continue the same line in second-order variational analysis to obtain the second-order optimality conditions. We specify these results to several optimization problems such as nonlinear programming, semidefinite programming, and calculus of variations. Throughout the talk, the ongoing research and open problems are discussed.
After joining Wayne State University, Ashkan Mohammadi studied Variational Analysis under the supervision of Prof. Boris Mordukhovich, one of the founders of Modern Variational Analysis. Dr. Mohammadi submitted his Ph.D. thesis under the title "Variational Analysis of Composite Optimization" in which he successfully developed a comprehensive second-order theory for constrained optimization. He solved the long-standing open problem of deriving the non-smooth chain rule for the second subderivative initiated by Terry Rockafellar in 1985. His results have been published in Transactions of the American Mathematical Society and SIAM Journal on Optimization.