Quasi-convex functions on subspaces and boundaries of quasi-convex sets
Published online by Cambridge University Press: 12 July 2007
Abstract
We embed truncations of the epi-graph of quasi-convex functions defined on linear subspaces E ⊂ MN × n of real matrices into MN × n to bound quasi-convex sets by the graph of the functions. We also characterize subspaces E on which all quasi-convex functions are convex and show, by using the Tarski–Seidenberg theorem in real algebraic geometry, that if dim (E) > N + n − 1, then there exist non-trivial quasi-convex functions on E.
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 134 , Issue 4 , August 2004 , pp. 783 - 799
- Copyright
- Copyright © Royal Society of Edinburgh 2004
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