From your requirements I cannot understand whether this qualifies: point that realizes the distance between a closed convex set and a given point (distance for a complete uniformly convex norm). Perhaps you should be more specific in your question.

From your requirements I cannot understand whether this qualifies: point that realizes the distance between a closed convex set and a given point (distance for a complete uniformly convex norm). Perhaps you should be more specific in your question.

Edit: I do not understand the meaning of "easy" for you. But I also know pratically nothing about coding theory. If you clarify "easy" for your context, perhaps someone else can give you more useful answers.