Projection oracle

Evaluate P𝒮(𝐱)P_\mathcal{S}(\mathbf{x}) for any 𝐱\mathbf{x}

P𝒮(𝐱)=argmin𝐲𝒮||𝐱𝐲||2P_\mathcal{S}(\mathbf{x})= \arg \min_{\mathbf{y}\in\mathcal{S}}||\mathbf{x}-\mathbf{y}||_2