Mathematical Sciences: Algorithms for Mathematical Programming

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This project will develop, analyze, and implement algorithms for solving mathematical programming problems. It is planned to focus on simplex algorithms, interior point algorithms, and methods that combine them. The research on simplex algorithms will be directed towards solving network flow problems including maximum flow, minimum flow, generalized network flow problems, and multicommodity flow problems. The research on interior point algorithms will concentrate on solving structured linear programs, exploring large step path-following algorithms, solving nonlinear programming problems. This research will involve theoretical analysis of the algorithms and their implementation and empirical testing. Extensive areas of society where operations research is required will benefit from this project.