On the convergence rate of the duality gap in a symmetric primal-dual potential reduction algorithm

In this short note, we prove that the global convergence rate of the duality gap in a symmetric primal-dual potential algorithm for linear programming, without line search, is no better than linear. More specifically, the convergence rate is no better than (1 − τ/√ n), where τ is a number between ze...

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Bibliographic Details
Published inOperations research letters Vol. 11; no. 5; pp. 289 - 291
Main Authors Zhu, Jishan, Huang, Siming
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 1992
Elsevier
Subjects
Applied sciences
Exact sciences and technology
Mathematical programming
Operational research and scientific management
Operational research. Management science
Reduction method
Primal dual method
Convergence rate
Linear programming
Duality
Potential function
Mathematical programming
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Summary:In this short note, we prove that the global convergence rate of the duality gap in a symmetric primal-dual potential algorithm for linear programming, without line search, is no better than linear. More specifically, the convergence rate is no better than (1 − τ/√ n), where τ is a number between zero and one.
ISSN:0167-6377
1872-7468
DOI:10.1016/0167-6377(92)90005-N