Abstract
The paper deals with with an optimization problem with a countably infinite system of Lipschitz equality constraints defined from an Asplund space to \(\mathbb {R}\). The main attention is paid to deriving new necessary optimality conditions in terms of stability conditions the constraint system. To do so, we reformulate the constraints to a generalized equation and we define a new weak constraint qualification based on the calmness property of multifunctions.
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Acknowledgments
The author would like to thank the Banach Algebra Center of Excellence for Mathematics, University of Isfahan.
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Movahedian, N. Necessary optimality conditions for countably infinite Lipschitz problems with equality constraint mappings. Optim Lett 10, 63–76 (2016). https://doi.org/10.1007/s11590-015-0855-x
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DOI: https://doi.org/10.1007/s11590-015-0855-x
Keywords
- Countably infinite Lipschitz problem
- Constraint qualification
- Optimality condition
- Calmness property
- Asplund space
- Separable Hilbert space