Approximate Optimality Conditions for Nonsmooth Optimization Problems
Ta Quang Son, Hua Khac Bao, Do Sang Kim · Taiwanese Journal of Mathematics · 2024
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.