Variational Analysis and its Applications

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This research project is devoted to the theory and applications of variational analysis, an active area in applied mathematics primarily concerned with optimization-related problems. It also applies variational techniques to the study of a broad range of problems that may not be of a variational nature. Since nonsmooth structures frequently and naturally appear in analysis and optimization, constructions and techniques of generalized differentiation lie at the heart of variational analysis and its applications. The project will mainly deal with developing the basic theory of variational analysis and generalized differentiation, with applications to important problems in optimization, control, stability, mechanics, and economics.Optimal decisions are required in various activities, including high-performance computing, manufacturing, environment and global change, etc. Variational analysis concerns mathematical methods of optimization that play a crucial role in many applications to complex systems in engineering, economics, and other areas of modern science and technology. This research project will focus on the development and application of efficient mathematical techniques for discovering optimal solutions in systems with complex structures. It particularly involves developing new methods of optimal control. This award is being jointly funded by the Division of Mathematical Sciences and the Directorate for Social, Behavioral, and Economic Sciences as part of the Mathematical Sciences Priority Area.