Quantitative Results on the Method of Averaged Projections
Explore a case study in "proof mining" focused on quantitative analysis of convex optimization problems. Delve into the convex feasibility problem, examining methods like alternating projections and averaged projections for finding common fixed points of firmly nonexpansive self-mappings in Hilbert or CAT(0) spaces. Investigate asymptotic regularity in cases where common fixed point sets are empty, and analyze the "in-between" scenario where the auxiliary mapping's fixed point set is non-empty. Learn about the application of these methods in CAT(0) spaces, including weak convergence and asymptotic regularity results. Gain insights into the proof mining contribution, which involves analyzing a trick to reduce the averaged projection method to the alternating projections method, particularly when dealing with projections onto closed, convex sets.