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quasiconvex functions

ESAIM: Control, Optimisation and Calculus of Variations (1)

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On the quasiconvex exposed points
Kewei Zhang
Journal:

ESAIM: Control, Optimisation and Calculus of Variations / Volume 6 / 2001

Published online by Cambridge University Press:

15 August 2002, pp. 1-19

Print publication:

2001
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The notion of quasiconvex exposed points is introduced for compact sets of matrices, motivated from the variational approach to material microstructures. We apply the notion to give geometric descriptions of the quasiconvex extreme points for a compact set. A weak version of Straszewicz type density theorem in convex analysis is established for quasiconvex extreme points. Some examples are examined by using known explicit quasiconvex functions.