TY - JOUR
T1 - On the self-duality and homogeneity of ellipsoidal cones
AU - Lu, Yue
AU - Chen, Jein Shan
N1 - Funding Information:
The author's work is supported by National Natural Science Foundation of China (Grant Number: 11601389), Doctoral Foundation of Tianjin Normal University (Grant Number: 52XB1513) and 2017-Outstanding Young Innovation Team Cultivation Program of Tianjin Normal University (Grant Number: 135202TD1703).
Publisher Copyright:
© 2018, Yokohama Publications.
PY - 2018
Y1 - 2018
N2 - The class of ellipsoidal cones, as an important prototype in closed convex cones, covers several practical instances such as second-order cone, circular cone and elliptic cone. In natural feature, it belongs to the category of nonsymmetric cones because it is non-self-dual under standard inner product. Nonetheless, it can be converted to a second-order cone, which is symmetric, by a transformation and vice versa. Is it possible to make an ellipsoidal cone to become self-dual by defining new setting of inner product? Is the class of ellipsoidal cones homogeneous? We provide affirmative answers for these two questions in this paper. As byproducts, its special cases such as circular cone and elliptic cone can be tackled likewise.
AB - The class of ellipsoidal cones, as an important prototype in closed convex cones, covers several practical instances such as second-order cone, circular cone and elliptic cone. In natural feature, it belongs to the category of nonsymmetric cones because it is non-self-dual under standard inner product. Nonetheless, it can be converted to a second-order cone, which is symmetric, by a transformation and vice versa. Is it possible to make an ellipsoidal cone to become self-dual by defining new setting of inner product? Is the class of ellipsoidal cones homogeneous? We provide affirmative answers for these two questions in this paper. As byproducts, its special cases such as circular cone and elliptic cone can be tackled likewise.
KW - Ellipsoidal cone
KW - Homogeneous cone
KW - Self-dual
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M3 - Article
AN - SCOPUS:85057193133
SN - 1345-4773
VL - 19
SP - 1355
EP - 1367
JO - Journal of Nonlinear and Convex Analysis
JF - Journal of Nonlinear and Convex Analysis
IS - 8
ER -