Mathematical Sciences: Optimization Theory

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The general subject area of this research is optimization theory and mathematical programming in particular. The overall objectives of the research are to advance the scientific understanding of the underlying properties of such problems, to develop effective computational methods for solving various classes of mathematical programming problems, and to propose ways in which the knowledge acquired can be implemented for the benefit of science and society. The methods employed in this project will include mathematical analysis, development and experimental testing of computer software for numerical solution of real-world problems. Mathematical programming is concerned with finding the best solution to problems with many variables and many constraints on such variables. Practical applications of such problems are found in virtually every branch of science and technology. The goal of the research is to extend the scope of mathematical programming methods and to make them more effective by enlarging the size of problems that can be handled, increasing the speed with which the computing is done, and improving the usefulness of the answers obtained.