Convex functions on compact $C^*$-convex sets

Document Type : Research Paper

Author

Department of Mathematics, Payame Noor University, P.O. Box 19395-3697 Tehran, Islamic Republic of Iran.

10.22072/wala.2020.120065.1268

Abstract

It is well known that if a real valued convex function on a compact convex domain
contained in the real numbers attains its maximum,
then it does so at least at one extreme point of its domain.
In this paper,
we consider a matrix convex function on a compact and $C^*$-convex set generated by self--adjoint matrices.
An important issue is so that this function on a compact and $C^*$-convex domain attains its maximum at a $C^*$-extreme point.

Keywords

References

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Wavelet and Linear Algebra
Volume 7, Issue 1
Spring- Summer
2020
Pages 57-62

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