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.

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