A class of new search directions for full-NT step feasible interior point method in semidefinite optimization

Abstract

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.