A smoothing-type algorithm for solving inequalities under the order induced by a symmetric cone

Journal of inequalities and applications

Nan Lu¹ 

关键词: Symmetric cone;    Euclidean Jordan algebra;    smoothing-type algorithm;    global convergence;    local quadratic convergence;   

DOI  :  10.1186/1029-242X-2011-4

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this article, we consider the numerical method for solving the system of inequalities under the order induced by a symmetric cone with the function involved being monotone. Based on a perturbed smoothing function, the underlying system of inequalities is reformulated as a system of smooth equations, and a smoothing-type method is proposed to solve it iteratively so that a solution of the system of inequalities is found. By means of the theory of Euclidean Jordan algebras, the algorithm is proved to be well defined, and to be globally convergent under weak assumptions and locally quadratically convergent under suitable assumptions. Preliminary numerical results indicate that the algorithm is effective. AMS subject classifications: 90C33, 65K10.

【 授权许可】

CC BY