Abstract
In this research article, a concept of $\varepsilon$-quasi subdifferential for locally Lipschitz functions is proposed. Calculuses of scalar product rule and sum rule for $\varepsilon$-quasi subdifferentials are investigated. A notion of $\varepsilon$-quasi normal set is introduced and its properties are presented. Based on the obtained results, optimality conditions for $\varepsilon$-quasi solutions in Karush–Kuhn–Tucker type of some classes of nonsmooth optimization problems are established. Several illustrative examples are also given.
Funding Statement
The first author was supported partially by Saigon University, Project No. CSA2022-04. The third author was supported by the National Research Foundation of Korea (NRF) Grant funded by the Korean Government (NRF-2019R1A2C1008672).
Citation
Ta Quang Son. Hua Khac Bao. Do Sang Kim. "Approximate Optimality Conditions for Nonsmooth Optimization Problems." Taiwanese J. Math. 28 (6) 1245 - 1266, December, 2024. https://doi.org/10.11650/tjm/240705
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