Nonsmooth Equations Approach to Optimization and Variational Inequality: Theory and Computation

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This project investigates the theory and computation of optimization problems and variational inequalities based on their equivalent formulation as a of nonsmooth equations. On the theoretical side, the goal is to gain, through the development of a comprehensive theory nonsmooth equations via their approximations, a better understanding of the sensitivity, stability, and other instrinsic properties of these mathematical programs. On the computational side, the goal is to develop, relying on generalizations of the classical Newton methods for smooth equations to the nonsmooth context, some robust, globally, locally quadratically convergent algorithms for solving these mathematical programs. The research is built on work in recent years which has demonstrated the fruitfulness of this nonsmooth-equations approach to variational inequalities, complementarity problems, and nonlinear programs.