On the P*(κ) horizontal linear complementarity problems over Cartesian product of symmetric cones. (3rd March 2016)

• Record Type: Journal Article
• Authors: Asadi, S.; Mansouri, H.; Darvay, Zs.; Zangiabadi, M.
• Is Part Of: Optimization methods and software. Volume 31:Number 2(2016)
• Page Start: 233
• Page End: 257
• Publication Date: 2016-03-03
• Subjects: horizontal linear complementarity problem -- Cartesian product of symmetric cones -- Euclidean Jordan algebra -- central trajectory -- sufficient linear operator; 90C51 -- 90C33; Mathematical optimization -- Periodicals; Algorithms -- Periodicals; 519.7
• DOI: 10.1080/10556788.2015.1058795
• Languages: English
• ISSNs: 1055-6788

Abstract

Abstract : The aim of this paper is to extend the theoretical framework of the horizontal 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 the property of a linear operator on a Euclidean Jordan algebra and its property 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 a linear 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.