# What's is this optimization function property called?

An optimization function $$f:\bigcup_{n \in \mathbf{N}} S^n \to \mathbf{R}$$ may have the property that given a domain $$P = \prod_{i=1}^N P_i$$ and the solution $$(m_i)_{i=1}^N = \underset{x \in P}{\operatorname{arg\,min}} f(x) \text{,}$$ the equality $$\large m_i=\underset{y \in P_i}{\operatorname{arg\,min}} f(y)$$ holds for all $i \in \{1..N\}$.

Is there a name for this property of $f$? Do you know of any relevant references?

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