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Normal Cone and Subdifferential with Respect to a Set at Infinity and Their Applications

Author

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  • Nguyen Le Hoang Anh

    (University of Science
    Vietnam National University)

  • Nguyen Canh Hung

    (University of Science
    Vietnam National University)

Abstract

In this paper, we first establish some properties of normal cones with respect to a set and derive calculus rules for subdifferentials with respect to a set at a reference point. Next, we introduce the concepts of normal cone with respect to a set to an epigraph at infinity, and subdifferential with respect to a set at infinity. Then, several properties of these notions at infinity are explored. Finally, we examine these tools at infinity to obtain necessary optimality conditions at infinity, the compactness of the optimal solution set, and the coercivity of the objective function for the underlying optimization problem under the unboundedness of its associated feasible set.

Suggested Citation

  • Nguyen Le Hoang Anh & Nguyen Canh Hung, 2025. "Normal Cone and Subdifferential with Respect to a Set at Infinity and Their Applications," Journal of Optimization Theory and Applications, Springer, vol. 206(3), pages 1-27, September.
    • Handle: RePEc:spr:joptap:v:206:y:2025:i:3:d:10.1007_s10957-025-02761-x
    DOI: 10.1007/s10957-025-02761-x
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