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Abstract
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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
5
4
+
1
𝑞 log 𝜀
−1) iteration complexity bound. Finally, the numerical
experiments of the proposed algorithm confirm th
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