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) (Darvay et al., in Optimization Letters, 12 (5), 1099-1116, 2018), we extend Kheirfam et al.’s feasible primal-dual path-following interior point algorithm for LO (Kheirfam et al., in Asian-European Journal of Mathematics, 1 (13), 2050014 (12 pages), 2020) 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 -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.

New efficient descent direction of a primal-dual path-following algorithm for linear programming

“…The authors proved the theoretical and numerical effectiveness of this new approach compared to other approaches. Furthermore, this technique has been extensively extended to other optimization problems (e.g., [9,14]...).…”

Interior-point algorithm for linear programming based on a new descent direction

“…Furthermore, the same authors in [26] extended this approach to symmetric optimization problems. Later, Kheirfam [18] extended the method to 𝑃 * (𝑘)-horizontal linear complementarity problems, while Guerra [16] applied it to the SDO case. For more related papers about Darvay and Takàcs' technique, we refer to (see e.g., [11,19,20]).…”