Algorithmic problems on convex sets
Many problems in mathematical programming can be formulated as problems on convex sets or convex bodies. Six kinds of problems are particularly important:[1]: Sec.2 optimization, violation, validity, separation, membership and emptiness. Each of these problems has a strong (exact) variant, and a weak (approximate) variant.
Strong variants
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Weak variants
References
- ^ Grötschel, Martin; Lovász, László; Schrijver, Alexander (1993), Geometric algorithms and combinatorial optimization, Algorithms and Combinatorics, vol. 2 (2nd ed.), Springer-Verlag, Berlin, doi:10.1007/978-3-642-78240-4, ISBN 978-3-642-78242-8, MR 1261419