Convergence of a Non-interior Continuation Algorithm for the Monotone SCCP  

作　　者：Nan Lu Zheng-Hai Huang 

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

出　　处：《Acta Mathematicae Applicatae Sinica》2010年第4期543-556,共14页应用数学学报（英文版）

基　　金：supported by the National Natural Science Foundation of China (Grants No.10571134 and 10871144);the Natural Science Foundation of Tianjin (Grant No.07JCYBJC05200)

摘　　要：It is well known that the symmetric cone complementarity problem（SCCP） is a broad class of optimization problems which contains many optimization problems as special cases.Based on a general smoothing function,we propose in this paper a non-interior continuation algorithm for solving the monotone SCCP.The proposed algorithm solves at most one system of linear equations at each iteration.By using the theory of Euclidean Jordan algebras,we show that the algorithm is globally linearly and locally quadratically convergent under suitable assumptions.It is well known that the symmetric cone complementarity problem（SCCP） is a broad class of optimization problems which contains many optimization problems as special cases.Based on a general smoothing function,we propose in this paper a non-interior continuation algorithm for solving the monotone SCCP.The proposed algorithm solves at most one system of linear equations at each iteration.By using the theory of Euclidean Jordan algebras,we show that the algorithm is globally linearly and locally quadratically convergent under suitable assumptions.

关 键 词：Symmetric cone complementarity problem non-interior continuation method global linear convergence local quadratic convergence 

分 类 号：O211.2[理学—概率论与数理统计] O221.2[理学—数学]