Constraint Reduction Reformulations for Projection Algorithms with Applications to Wavelet Construction

We introduce a reformulation technique that converts many-set feasibility problem into an equivalent two-set problem. This involves reformulating the original by replacing pair of its constraint sets with their intersection, before applying Pierra’s classical product space reformulation. The step combining two reduces dimension spaces. refer to this as reduction and use it obtain constraint-reduced variants well-known projection algorithms such Douglas–Rachford algorithm method alternating projections, among others. prove global convergence in presence convexity local nonconvex setting. In order analyze method, we generalize result which guarantees composition projectors onto subspaces is projector intersection. Finally, apply versions projections solve wavelet problems then compare performance usual variants.