No Gap Second-Order Optimality Conditions for Circular Conic Programs |
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Authors: | Yue Lu Ning Zhang |
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Institution: | 1. School of Mathematical Sciences, Tianjin Normal University, Tianjin, China;2. Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Hong Kong |
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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. |
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Keywords: | Circular cone no gap second-order optimality conditions second-order tangent set “sigma” term tangent cone |
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