One of the widely used convex optimization algorithms is
projections onto convex sets (POCS). This algorithm is employed to recover/synthesize a signal satisfying simultaneously several convex constraints. Let f_i be the indicator function of non-empty closed convex set C_i modeling a constraint. This reduces to convex feasibility problem, which require us to find a solution such that it lies in the intersection of all convex sets C_i. In POCS method each set C_i is incorporated by its
projection operator P_{C_i}. So in each
iteration x is updated as : x_{k+1} = P_{C_1} P_{C_2} \cdots P_{C_n} x_k However beyond such problems
projection operators are not appropriate and more general operators are required to tackle them. Among the various generalizations of the notion of a convex projection operator that exist, proximal operators are best suited for other purposes. == Examples ==