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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]

The aim of this paper is to extend the theoretical framework of thehorizontal linear complementarity problem over Cartesian product of symmetric cones (Cartesian-SCHLCP). The concepts of column and row sufficiency are defined for a linear operator on a Euclidean Jordan algebra. Some connections between theproperty of a linear operator on a Euclidean Jordan algebra and itsproperty as well as its column sufficiency are presented. Then these definitions and connections are generalized to a pair of linear operators determining the Cartesian-SCHLCP. It is also demonstrated that the Cartesian-SCHLCP can be equivalent with alinear complementarity problem over Cartesian product of symmetric cones (Cartesian-SCLCP), in a certain sense. Finally, based on some obtained results and using a suitable potential function, the main task of the paper is done, which is to show that the central trajectory of the Cartesian-SCHLCP exists and is unique. Therefore, we open the way for presenting and extending the interior-point methods for the Cartesian-SCHLCP. [ABSTRACT FROM AUTHOR]