No Gap Second-Order Optimality Conditions for Circular Conic Programs. (27th July 2019)

• Record Type: Journal Article
• Authors: Lu, Yue; Chen, Jein-Shan; Zhang, Ning
• Is Part Of: Numerical functional analysis and optimization. Volume 40:Number 10(2019)
• Page Start: 1113
• Page End: 1135
• Publication Date: 2019-07-27
• Subjects: Circular cone -- no gap second-order optimality conditions -- second-order tangent set -- "sigma" term -- tangent cone; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2018.1552965
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: 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.