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2022 | OriginalPaper | Buchkapitel

Nonsmooth Mathematical Programs with Vanishing Constraints in Banach Spaces

verfasst von: Vivek Laha, Vinay Singh, Yogendra Pandey, S. K. Mishra

Erschienen in: High-Dimensional Optimization and Probability

Verlag: Springer International Publishing

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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.
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Metadaten
Titel
Nonsmooth Mathematical Programs with Vanishing Constraints in Banach Spaces
verfasst von
Vivek Laha
Vinay Singh
Yogendra Pandey
S. K. Mishra
Copyright-Jahr
2022
DOI
https://doi.org/10.1007/978-3-031-00832-0_13

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