Abstract
Convex sets and convex functions are typical objects of study in mathematical programming, convex analysis, and related areas. Here are some key questions one encounters frequently:
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Given a point y and a set K, is y a member of K, i. e., is y contained in K ?
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If y is not a member of K, find a hyperplane separating y from K.
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Given a linear inequality, is it valid for each vector in K ?
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Given a linear function, find a point maximizing (or minimizing) the function on K.
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Given a convex function, find its minimum.
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© 1988 Springer-Verlag Berlin Heidelberg
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Grötschel, M., Lovász, L., Schrijver, A. (1988). Algorithmic Aspects of Convex Sets: Formulation of the Problems. In: Geometric Algorithms and Combinatorial Optimization. Algorithms and Combinatorics, vol 2. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-97881-4_3
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DOI: https://doi.org/10.1007/978-3-642-97881-4_3
Publisher Name: Springer, Berlin, Heidelberg
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