Research Initiation: Interior Point Algorithms for Linear and Convex Programming

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Since the development of Karmarkar's algorithm for linear programming, interest is rejuvenated in the interior point algorithms for solving linear and convex programming problems. Several variants of interior point algorithms have shown considerable promise to achieve substantial improvement in efficiency over the simplex method for linear programming problems. Through this proposal, we request funds to further continue our study of the theoretical properties and the computational effectiveness of these algorithms. We intend to effectively integrate the theory developed in our previous work with our experimental experience to develop a general purpose code for solving these problems.^R JUSTIFICATION