Projection on convex sets

tags
Optimization

To solve the problem of finding \(x \in \mathbb{R}^n\) such that \(x\in C \cap D\) where \(C\) and \(D\) are closed convex sets, we project a candidate solution onto \(D\) and \(C\) successively until it converges to a point in the intersection.

\[ x_{k+1} = \mathcal{P}_C (\mathcal{P}_D (x_k)) \]

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