Abstract
In this chapter certain approximations of sets are considered which are very useful for the formulation of optimality conditions. We investigate so-called tangent cones which approximate a given set in a local sense. First, we discuss several basic properties of tangent cones, and then we present optimality conditions with the aid of these cones. Finally, we formulate a Lyusternik theorem.
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Notes
- 1.
M.G. Bouligand, “Sur les surfaces dépourvues de points hyperlimites (ou: un thèorème d’existence du plan tangent)”, Ann. Soc. Polon. Math. 9 (1930) 32–41.
F. Severi remarked that he has independently introduced this notion (F. Severi, “Su alcune questioni di topologia infinitesimale”, Ann. Soc. Polon. Math. 9 (1930) 97–108).
- 2.
L.A. Lyusternik, “Conditional extrema of functionals”, Mat. Sb. 41 (1934) 390–401.
References
J. Werner, Optimization - theory and applications (Vieweg, Braunschweig, 1984).
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Jahn, J. (2020). Tangent Cones. In: Introduction to the Theory of Nonlinear Optimization. Springer, Cham. https://doi.org/10.1007/978-3-030-42760-3_4
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DOI: https://doi.org/10.1007/978-3-030-42760-3_4
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