Volume 56, Number 6, November-December 2022
|Page(s)||3955 - 3971|
|Published online||25 November 2022|
A class of new search directions for full-NT step feasible interior point method in semidefinite optimization
Département de Recherche Opérationnelle, Faculté des Mathématiques et d’Informatique, Université Mohamed El Bachir El Ibrahimi, Bordj Bou Arréridj, El Anasser 34030, Algérie
Accepted: 26 October 2022
In this paper, based on Darvay et al.’s strategy for linear optimization (LO) (Z. Darvay and P.R. Takács, Optim. Lett. 12 (2018) 1099–1116.), we extend Kheirfam et al.’s feasible primal-dual path-following interior point algorithm for LO (B. Kheirfam and A. Nasrollahi, Asian-Eur. J. Math. 1 (2020) 2050014.) to semidefinite optimization (SDO) problems in order to define a class of new search directions. The algorithm uses only full Nesterov-Todd (NT) step at each iteration to find an ε-approximated solution to SDO. Polynomial complexity of the proposed algorithm is established which is as good as the LO analogue. Finally, we present some numerical results to prove the efficiency of the proposed algorithm.
Mathematics Subject Classification: 90C51 / 90C25 / 90C22
Key words: Semidefinite optimization / interior point method / full Nesterov-Todd step / new search directions / algebraic equivalent transformation / polynomial complexity
© The authors. Published by EDP Sciences, ROADEF, SMAI 2022
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