Abstract
Definition of a convex set. The empty set is, by definition, convex. The first set is convex, while the second is not convex. Properties of convex sets. (a and b are real numbers.) Definition of a convex combination of vectors. co(S) is the convex hull of a set S in ℝn.
Keywords
- Convex Hull
- Hessian Matrix
- Convex Combination
- Strict Convexity
- Separation Theorem
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References
For concave/convex and quasiconcave/quasiconvex functions, see e.g. Simon and Blume (1994) or Sydsæter et al. (2005). For pseudoconcave and pseudoconvex functions, see e.g. Simon and Blume (1994), and their references. For special results on convex sets, see Nikaido (1968) and Takayama (1985). A standard reference for convexity theory is Rockafellar (1970).
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© 2010 Springer-Verlag Berlin Heidelberg
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Sydsæter, K., Strøm, A., Berck, P. (2010). Convexity. In: Economists’ Mathematical Manual. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-28518-2_13
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DOI: https://doi.org/10.1007/978-3-540-28518-2_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-26088-2
Online ISBN: 978-3-540-28518-2
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