# 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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