Abstract
In this paper, a nonsmooth nonconvex robust optimization problem is considered. Using the idea of pseudo-differential, nonsmooth versions of the Robinson, Mangasarian–Fromovitz and Abadie constraint qualifications are introduced and their relations with the existence of a local error bound are investigated. Based on the pseudo-differential notion, new necessary optimality conditions are derived under the Abadie constraint qualification. Moreover, an example is provided to clarify the results.
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The first-named author was partially supported by a grant from IPM (NO. 1400490042).
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Hejazi, M.A., Movahedian, N. On constraint qualifications and optimality conditions for robust optimization problems through pseudo-differential. Optim Lett 18, 705–726 (2024). https://doi.org/10.1007/s11590-023-02078-6
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DOI: https://doi.org/10.1007/s11590-023-02078-6