Primal-Dual Interior Point Algorithms for Mathematical Programming

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This project will produce theoretical and numerical results on interior point methods for linear programming and other mathematical programming problems. Specific objectives include: a) Development of a primal-dual algorithm that not only possesses the currently best optimal complexity bound but also the best achievable asymptotic convergence rate. b) Development of techniques that can effectively utilize available information at each iteration and overall efficiency, and c) Development of techniques that effectively handle the singularity at non-vertex or degenerate vertex solutions. The methodology for this research will constantly combine numerical experimentation with theoretical analysis, and will study primal-dual interior point linear programming algorithms from the point of view of solving a nonlinear system of equations. Results of this project shall have a significant impact in the design of telecomunication networks, large scale logistic planning, and scheduling.