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In this paper, we present a feasible predictor-corrector interior-point method for symmetric cone optimization problem in the large neighbourhood of the central path. The method is generalization of Ai-Zhang's predictor-corrector algorithm to the symmetric cone optimization problem. Starting with a feasible point in given large neighbourhood of the central path, the algorithm still terminates in at most iterations. This matches the best known iteration bound that is usually achieved by short-step methods, thereby, closing the complexity gap between long- and short-step interior-point methods for symmetric cone optimization. The preliminary numerical results on a selected set of NETLIB problems show advantage of the method in comparison with the version of the algorithm that is not based on the predictor-corrector scheme. [ABSTRACT FROM AUTHOR]

In this paper, we propose a non-monotone line search method for solving optimization problems on Stiefel manifold. The main novelty of our approach is that our method uses a search direction based on a linear combination of descent directions and a Barzilai-Borwein line search. The feasibility is guaranteed by projecting each iterate on the Stiefel manifold through SVD (singular value decomposition) factorizations. Some theoretical results for analysing the algorithm are presented. Finally, we provide numerical experiments for comparing our algorithm with other state-of-the-art procedures. The code is available online. The experimental results show that the proposed algorithm is competitive with other approaches and for particular problems, the computational performance is better than the state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]