EXTENSION OF SMOOTHING NEWTON ALGORITHMS TO SOLVE LINEAR PROGRAMMING OVER SYMMETRIC CONES  

作　　者：Zhenghai HUANG Xiaohong LIU 

机构地区：[1]Department of Mathematics, School of Science, Tianjin University, Tianjin 300072, China

出　　处：《Journal of Systems Science & Complexity》2011年第1期195-206,共12页系统科学与复杂性学报（英文版）

基　　金：This research is supported by the National Natural Science Foundation of China under Grant No. 10871144 and the Natural Science Foundation of Tianjin under Grant No. 07JCYBJC05200.

摘　　要：There recently has been much interest in studying some optimization problems over symmetric cones. This paper deals with linear programming over symmetric cones （SCLP）. The objective here is to extend the Qi-Sun-Zhou＇s smoothing Newton algorithm to solve SCLP, where characterization of symmetric cones using Jordan algebras forms the fundamental basis for our analysis. By using the theory of Euclidean Jordan algebras, the authors show that the algorithm is globally and locally quadratically convergent under suitable assumptions. The preliminary numerical results for solving the second-order cone programming are also reported.

关 键 词：Euclidean Jordan algebra linear programming smoothing algorithm symmetric cone. 

分 类 号：O221.1[理学—运筹学与控制论] TM744[理学—数学]