Recent years have witnessed a significant progress in modern variational analysis, which has become a fruitful area of mathematics with a strong emphasis on applications. The project mainly concerns the development of advanced variational principles and techniques with their broad applications to various problems in optimization and equilibria (including bilevel and semi-infinite programming, optimization and equilibrium problems with equilibrium constraints, multiobjective optimization); well-posedness and conditioning of numerical algorithms; optimal control of ordinary differential, functional differential, and partial differential systems, etc. Since nonsmooth functions and set-valued mappings appear naturally and frequently in applying advanced variational principles and techniques, the project strongly addresses generalized differential theory for such nonstandard objects.
Optimization/variational principles and techniques developed in this project primarily aim at applications to real-life problems arising in economics, environmental science, electricity markets, engineering, and mechanics. By modeling such problems in the forms suitable for applications of advanced variational techniques and developing theoretical and numerical methods for their study, the project will solve a number of real-life problems of practical importance arising in the aforementioned areas.
