An alternative approach for a distance inequality associated with the second-order cone and the circular cone

Journal of Inequalities and Applications

Yen-chi Roger Lin¹  Jein-Shan Chen¹  Xin-He Miao² 

[1] Department of Mathematics, National Taiwan Normal University;Department of Mathematics, Tianjin University;

关键词: second-order cone;    circular cone;    projection;    distance;   

DOI  :  10.1186/s13660-016-1243-5

来源: DOAJ

【 摘 要 】

Abstract It is well known that the second-order cone and the circular cone have many analogous properties. In particular, there exists an important distance inequality associated with the second-order cone and the circular cone. The inequality indicates that the distances of arbitrary points to the second-order cone and the circular cone are equivalent, which is crucial in analyzing the tangent cone and normal cone for the circular cone. In this paper, we provide an alternative approach to achieve the aforementioned inequality. Although the proof is a bit longer than the existing one, the new approach offers a way to clarify when the equality holds. Such a clarification is helpful for further study of the relationship between the second-order cone programming problems and the circular cone programming problems.

【 授权许可】

Unknown