Some applications of directional subdifferentials at infinity to vector optimization problems
DOI:
https://doi.org/10.56764/hpu2.jos.2026.5.01.76-86Abstract
This paper presents a comprehensive investigation into several advanced applications of variational analysis, with a particular focus on the roles of special normal cones and directional subdifferentials at infinity. By extending classical tools of nonsmooth and variational analysis to unbounded settings, we establish directional optimality conditions at infinity and derive sufficient conditions ensuring the existence and compactness of global solution sets for vector optimization problems. The theoretical results obtained contribute to a deeper understanding of optimization behavior in asymptotic regimes. Furthermore, illustrative examples are provided to demonstrate the validity and applicability of the proposed results, highlighting their potential use in future research on infinite-dimensional and unbounded optimization problems.
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Copyright (c) 2026 Ngoc-Kien Le, Van-Nghi Tran, Van-Hao Nguyen
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