Primal-Dual  Algorithms for Linear Programming Based on the Logarithmic  Barrier Method<br/>

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Primal-Dual Algorithms for Linear Programming Based on the Logarithmic Barrier Method

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 39699 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Mahdavi Amiri, Nezameddin
Abstract:
We deal with primal-dual interior point methods for solving the linear programming problem.Taken from recent literature on interior point methods, we discuss a short-step and a long-step path-following primal-dual method and show how to have polynomial-time bounds for both methods. The iteration bounds are for the short-step variant and for the long-step variant. In the analysis of both variants, a new proximity measure is used, which is closely related to the Euclidean norm of the scaled search direction vectors. The analysis of the long-step method depends strongly on the fact that the usual search directions form a descent direction for the so-called primal-dual logarithmic barrier function. We implement the method in Matlab7.3 environment and test the programs on several test problems.
Keywords:
Linear Programming ; Pol Ynomial Algorithm ; Interior Point Method ; Primal-Dual Algorithm ; Logarithmic Barrier Function

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