Let <InlineEquation ID="IEq1270"> <EquationSource Format="TEX">$$\mathbb{M}_{m,n}$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <msub> <mi mathvariant="double-struck">M</mi> <mrow> <mi>m</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> </math> </EquationSource> </InlineEquation> be the linear space of real matrices of dimension m × n. A variational problem that arises quite often in applications is that of minimizing a real-valued function f on some feasible set <InlineEquation ID="IEq128"> <EquationSource Format="TEX">$$\Upomega\subseteq \mathbb{M}_{m,n}.$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mi mathvariant="normal">Ω</mi> <mo>⊆</mo> <msub> <mi mathvariant="double-struck">M</mi> <mrow> <mi>m</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub>...</mo></mrow></math></equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation>

We introduce an axiomatic formalism for the concept of the center of a set in a Euclidean space. Then we explain how to exploit possible symmetries and possible cyclicities in the set in order to localize its center. Special attention is paid to the determination of centers in cones of matrices....