Abstract
This last chapter addresses several issues related to the previous chapters. The first part is mainly aimed at deriving optimality conditions for a convex optimization problem, posed in an lcs, with an arbitrary number of constraints. The approach taken is to replace the set of constraints with a unique constraint via the supremum function. Subsequently, we appeal to the properties of the subdifferential of the supremum function that has been exhaustively studied in the previous chapters. With this goal, we extend to infinite convex systems two constraint qualifications that are crucial in linear semi-infinite programming. The first, called the Farkas–Minkowski property, is global in nature, while the other is a local property, called locally Farkas–Minkowski. We obtain two types of Karush–Kuhn–Tucker (KKT, in brief) optimality conditions: asymptotic and non-asymptotic.
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Correa, R., Hantoute, A., López, M.A. (2023). Miscellaneous. In: Fundamentals of Convex Analysis and Optimization. Springer Series in Operations Research and Financial Engineering. Springer, Cham. https://doi.org/10.1007/978-3-031-29551-5_8
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DOI: https://doi.org/10.1007/978-3-031-29551-5_8
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Publisher Name: Springer, Cham
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Online ISBN: 978-3-031-29551-5
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