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DOI: 10.23952/cot.2024.28
Received August 8, 2023; Accepted December 11, 2023; Published online April 11, 2024
Abstract. In this paper, we study some new characterizations for the weak subdifferentials with lower Lipschitz functions in real normed space and its applications to nonconvex mathematical programming problems having set, inequality and equality constraints. First, some new properties of the weak subdifferential and the argumented normal cone are formulated. Second, the fuzzy sum rules, in general, in terms of weak subdifferentials are proposed. Third, we derive some necessary and sufficient optimality conditions for having the global minimum. Finally, some necessary and sufficient optimality conditions for the (weak) efficiency of such problems are obtained.
How to Cite this Article:
T.V. Su, Efficiency conditions for nonconvex mathematical programming problems via weak subdifferentials, Commun. Optim. Theory 2024 (2024) 28.