# I have a doubt regarding a constrained optimisation problem. Suppose my original constrained mi

I have a doubt regarding a constrained optimisation problem.

Suppose my original constrained minimisation problem is

I would like to know if this equivalent to solving the unconstrained minimisation problem
$\underset{x}{min}f\left(3,x\right)$
If not, when are these two problems equivalent?
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lisicw2
The problems are certainly not equivalent in general. Take to be given by

and to be given by

for instance. Then the minimum value of is 9 , and occurs when , whereas

is , and occurs when . I agree with Michal Adamszek's comment that the two problems will almost never be equivalent.