Robust, Global Nonsmooth Newton Methods for Variational Inequality, Complementarity and Nonlinear Programming Problems

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This project is concerned with the development, analysis and implementation of a robust, globally convergent, Nonsmooth Equation Based, Successive Quadratic Programming (NE/SQP) method for solving the finite-dimensional variational inequality, nonlinear complementarily and nonlinear programming problems. The method is an iterative descent algorithm that is based on a common reformulation of these three important classes of mathematical programs as a system of nonsmooth equations, to which an extension/modification of the classical Gauss-Newton method for smooth equations is applied. Some preliminary convergence results have been established, and computational experience with previous global non-smooth Newton methods suggests that the new and improved NE/SQP method could become a major practical tool for solving various kinds of systems engineering and economics equilibrium problems, as well as for a variety of optimization problems arising from diverse disciplines in science and engineering.