2016-10-01
Inner and outer approximation of convex sets using alignment
Publication
Publication
Optimization Letters , Volume 10 - Issue 7 p. 1403- 1416
We show that there exists, for each closed bounded convex set C in the Euclidean plane with nonempty interior, a quadrangle Q having the following two properties. Its sides support C at the vertices of a rectangle r and at least three of the vertices of Q lie on the boundary of a rectangle R that is a dilation of r with ratio 2. We will prove that this implies that quadrangle Q is contained in rectangle R and that, consequently, the inner approximation r of C has an area of at least half the area of the outer approximation Q of C. The proof makes use of alignment or Schüttelung, an operation on convex sets.
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| , , , , , | |
| doi.org/10.1007/s11590-015-0941-0, hdl.handle.net/1765/87969 | |
| Optimization Letters | |
| Organisation | Department of Econometrics |
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Brinkhuis, J. (2016). Inner and outer approximation of convex sets using alignment. Optimization Letters, 10(7), 1403–1416. doi:10.1007/s11590-015-0941-0 |
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