Are these two functions equal to each other?

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Say I need to optimize this function $\underset{a,b}{\operatorname{argmax}} g(a,b)$, where $g(a,b)\geq 0 \ \forall a,b$. Could I transform it into $\underset{a}{\operatorname{argmax}}(\underset{b}{\operatorname{argmax} g(a,b)})$ where $g(a,b)\geq 0 \ \forall a,b$ ? If yes, can it be proved?