Second-Order Variational Analysis and Its Applications

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This project aims to develop efficient tools of mathematical analysis to investigate challenging problems arising in optimization, systems control, and other fields of applied mathematics unified under the name of variational analysis. This new form of analysis employs generalized differential calculus when the standard calculus methods are not available. The main motivation for developing these tools of analysis is to solve a number of practical problems of engineering, mechanics, and behavioral sciences. Results of this project arm researchers and practitioners with new machinery that make it possible to solve problems that provide valuable insight to practical issues.This project focuses on second-order variational analysis, which has been largely underinvestigated from both viewpoints of theoretical studies and practical applications. It carries out a systematic development of generalized differential tools of second-order analysis, with applications to the design and justification of numerical algorithms in nonsmooth optimization and related areas. Among other directions of research, the project applies second-order variational analysis to broad classes of finite-dimensional and infinite-dimensional variational systems, which go far beyond optimization and optimal control. Results will be beneficial to both applied mathematics and applied science communities.