No abstract

In this paper, we propose a large-update primal-dual interior point algorithm for convex quadratic semidefiniteoptimization (CQSDO) based on a new parametric kernel function. This kernel function is a parameterized version of the kernel function introduced by M.W. Zhang (Acta Mathematica Sinica. 28: 2313-2328, 2012) for CQSDO. The investigation according to it generating the best known iteration bound O for large-update methods. Thus improves the iteration bound obtained by Zhang for large-update methods. Finally, we present few numerical results to show the efficiency of the proposed algorithm.

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.