An efficient second-order predictor–corrector infeasible primal–dual IPM algorithm with large iteration path updates for solving well-known SDO problems

In this paper, we propose a second-order predictor–corrector infeasible interior-point algorithm for semidefinite optimization in a new large neighborhood. The new large neighborhood, which is based on the spectral norm, is wider than the popular large neighborhoods based on the negative pseudo-infinity norm and the Frobenius norm. In each iteration, our algorithm calculates a new predictor direction using two modified systems and Yang et al. strategy. Then, this algorithm calculates a second-order corrector direction using the directions obtained in the predictor step. The iterates are determined by taking the largest possible step lengths along the search directions within the new large neighborhood. We prove that the algorithm is globally convergent and has $O(n^{\frac{5}{4}+\frac{1}{q}}log{\varepsilon }^{-1})$ iteration complexity bound. Finally, the numerical experiments of the proposed algorithm confirm the efficiency and reliability of this approach.