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- W4289690829 abstract "In this chapter, we study the optimization problems with equality, inequality, and vanishing constraints in a Banach space where the objective function and the binding constraints are either differentiable at the optimal solution or Lipschitz near the optimal solution. We derive nonsmooth Karush–Kuhn–Tucker (KKT) type necessary optimality conditions for the above problem where Fréchet (or Gâteaux or Hadamard) derivatives are used for the differentiable functions and the Michel-Penot (M-P) subdifferentials are used for the Lipschitz continuous functions. We also introduce several modifications of some known constraint qualifications like Abadie constraint qualification, Cottle constraint qualification, Slater constraint qualification, Mangasarian–Fromovitz constraint qualification, and linear independence constraint qualification for the above mentioned problem which is called as the nonsmooth mathematical programs with vanishing constraints (NMPVC) in terms of the M-P subdifferentials and establish relationships among them." @default.
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- W4289690829 date "2022-01-01" @default.
- W4289690829 modified "2023-10-17" @default.
- W4289690829 title "Nonsmooth Mathematical Programs with Vanishing Constraints in Banach Spaces" @default.
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- W4289690829 doi "https://doi.org/10.1007/978-3-031-00832-0_13" @default.
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