Abstract
Separation theorems involving convex sets is an important topic in optimization. The duality theory of convex programming depends on them, and the various optimality conditions in optimization theory, from the Fritz John and Karush–Kuhn–Tucker (KKT) conditions to the Pontryagin maximum principle, can be obtained from them. In addition, the familiar Hahn–Banach theorem, which is one of the cornerstones in functional analysis with an enormous number of applications in the field, is an analytic form of a separation theorem.
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© 2010 Springer New York
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Güler, O. (2010). Separation of Convex Sets. In: Foundations of Optimization. Graduate Texts in Mathematics, vol 258. Springer, New York, NY. https://doi.org/10.1007/978-0-387-68407-9_6
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DOI: https://doi.org/10.1007/978-0-387-68407-9_6
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Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-34431-7
Online ISBN: 978-0-387-68407-9
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