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

Nguyen Le Hoang Anh () and Nguyen Canh Hung ()
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Nguyen Le Hoang Anh: University of Science
Nguyen Canh Hung: University of Science

Journal of Optimization Theory and Applications, 2025, vol. 206, issue 3, No 21, 27 pages

Abstract: 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.

Keywords: Limiting subdifferentials; Normal cones and Subdifferentials with respect to a set; Calculus rules; Optimality conditions; Compactness; Coercivity (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-025-02761-x

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