Suppose we have a constrained convex optimization problem $min_{x \in \mathcal{C}}f(x)$. Is it correct to first solve the unconstrained problem ($\tilde{x}=argmin_{x}f(x)$) and then project the solution to the feasible set ($\hat{x}=\Pi_\mathcal{C}(\tilde{x})$) in order to find an optimal solution to the original problem?
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Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. – Community Jun 12 '23 at 07:21