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Quasi-convex functions on subspaces and boundaries of quasi-convex sets

Published online by Cambridge University Press:  12 July 2007

Kewei Zhang
Department of Mathematics, University of Sussex, Brighton BN1 9RF, UK (


We embed truncations of the epi-graph of quasi-convex functions defined on linear subspaces EMN × 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.

Research Article
Copyright © Royal Society of Edinburgh 2004

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