Let us assume that we have the following optimization problem: $$ \max_{x,y,z}f\left(x,y,z\right) $$ subject to: $$ x+y+z=4 $$ In the above, the constraint holds with equality. Is it true to say that we only need to maximize over two arguments, as the third one is pinned down by the constraint? In other words, is it sufficient to choose an optimal $x^{*}$, $y^{*}$ and get $z^{*}$ from the constraint simply?
2026-02-27 14:30:36.1772202636
Number of arguments in constrained optimization
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