Postponing the Choice of the Barrier Parameter in Mehrotra-Type Predictor–Corrector Algorithms

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Rezaee, Saeed | 2011

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 41222 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Mahdavi Amiri, Nezam
Abstract:
In some cases, Mehrotra’s predictor–corrector algorithm might make very small steps in order to keep the iterate in a certain neighborhood of the central path, and thus implying the inefficiency of the algorithm. In this study, a different approach for controlling the iterates on the algorithm is investigated, which was recently introduced by Salahi and Terlaky. The approach is based on postponing the choice of the barrier parameter. To do so, a step size is fixed in the corrector step and then by solving a one dimensional optimization problem, the barrier parameter is computed. Finally, using the computed barrier parameter, the next step is taken. It has already been proved that the new algorithm’s complexity is O(n^2 log⁡〖n/ε〗). For this algorithm, a superlinear rate of convergence has been established. This method is implemented in Matlab and the numerical results are presented
Keywords:
Predictor-Corrector Method ; Superlinear Convergence ; Mehrotra-Type Algorithm ; Polynomial Complexity