TY - JOUR
T1 - No Gap Second-Order Optimality Conditions for Circular Conic Programs
AU - Lu, Yue
AU - Chen, Jein Shan
AU - Zhang, Ning
N1 - Funding Information:
The first author is supported by the Doctoral Foundation of Tianjin Normal University [grant number 52XB1513], the National Natural Science Foundation of China [grant number 11601389, 11871372]. The second author is supported by Ministry of Science and Technology, Taiwan.
Publisher Copyright:
© 2019, © 2019 Taylor & Francis Group, LLC.
PY - 2019/7/27
Y1 - 2019/7/27
N2 - In this article, we study the second-order optimality conditions for a class of circular conic optimization problem. First, the explicit expressions of the tangent cone and the second-order tangent set for a given circular cone are derived. Then, we establish the closed-form formulation of critical cone and calculate the “sigma” term of the aforementioned optimization problem. At last, in light of tools of variational analysis, we present the associated no gap second-order optimality conditions. Compared to analogous results in the literature, our approach is intuitive and straightforward, which can be manipulated and verified. An example is illustrated to this end.
AB - In this article, we study the second-order optimality conditions for a class of circular conic optimization problem. First, the explicit expressions of the tangent cone and the second-order tangent set for a given circular cone are derived. Then, we establish the closed-form formulation of critical cone and calculate the “sigma” term of the aforementioned optimization problem. At last, in light of tools of variational analysis, we present the associated no gap second-order optimality conditions. Compared to analogous results in the literature, our approach is intuitive and straightforward, which can be manipulated and verified. An example is illustrated to this end.
KW - Circular cone
KW - no gap second-order optimality conditions
KW - second-order tangent set
KW - tangent cone
KW - “sigma” term
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U2 - 10.1080/01630563.2018.1552965
DO - 10.1080/01630563.2018.1552965
M3 - Article
AN - SCOPUS:85064819883
SN - 0163-0563
VL - 40
SP - 1113
EP - 1135
JO - Numerical Functional Analysis and Optimization
JF - Numerical Functional Analysis and Optimization
IS - 10
ER -