Projections onto convex sets is a mathematical concept often used in optimization, functional analysis, and convex geometry. The idea centers around finding a point in a convex set that is closest to a given point outside that set.
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Projections onto convex sets is an iterative feasibility method that successively applies a Euclidean projection onto a convex set to each closed convex constraint set. With two sets it uses . It seeks a point in the intersection; a single projection onto one set is a different operation, and the method does not generally compute the closest intersection point to the initial iterate.