Abstract
This chapter deals with the extension of the Tent Method to Banach spaces. The Abstract Extremal Problem is formulated as an intersection problem. The subspaces in the general positions are introduced. The necessary condition of the separability of a system of convex cones is derived. The criterion of separability in Hilbert spaces is presented. Then the analog of the Kuhn–Tucker Theorem for Banach spaces is discussed in detail.
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References
Boltyanski, V. (1972a), ‘The separation property for a system of convex cones’, Izv. Akad. Nauk Arm. SSR, Ser. Fiz.-Mat. Nauk 7(4), 250–257 (in Russian).
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Kuhn, H., & Tucker, A. (1951), ‘Nonlinear programming’, in Proceedings of the Second Berkeley Symposium on Math. Statistics and Probability, University of California Press, Berkeley, pp. 481–492.
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Boltyanski, V.G., Poznyak, A.S. (2012). Extremal Problems in Banach Spaces. In: The Robust Maximum Principle. Systems & Control: Foundations & Applications. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-8152-4_7
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DOI: https://doi.org/10.1007/978-0-8176-8152-4_7
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-0-8176-8151-7
Online ISBN: 978-0-8176-8152-4
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