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The authors declare that none of the authors have any competing interests in the manuscript.
All authors participated in its design and coordination and helped to draft the manuscript. All authors read and approved the final manuscript.
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.
Facchinei, F, Pang, J: Finite-Dimensional Variational Inequalities and Complementarity Problems. Springer, New York (2003) MATH
Faraut, U, Korányi, A: Analysis on Symmetric Cones. Oxford Mathematical Monographs. Oxford University Press, New York (1994) MATH
Nesterov, Y: Towards nonsymmetric conic optimization. Discussion paper 2006/28, Center for Operations Research and Econometrics (2006)
- An alternative approach for a distance inequality associated with the second-order cone and the circular cone
Yen-chi Roger Lin
- Springer International Publishing
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