Algorithms, Applications and Theory of Mathematical Programming

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Parallel algorithms will be developed for general nonlinear programs as well as for linear and quadratic programs. Emphasis will be placed on the recently proposed idea of constraint distribution among parallel processors as well as inexact and exact matrix splitting methods for the linear complementarity problem. Applications of mathematical programming to pattern recognition and neural networks will also be made, where the potential of optimization algorithms has not been fully realized. Particular attention will be given to medical diagnostic problems, some of which have been successfully solved by linear programming. Mathematical theory that is needed for the above algorithms and applications will be developed and sharpened. An important and promising area to be focused on is that of error bounds for various types of mathematical programs.