Theory and Applications of Convex and Non-convex Feasibility Problems

Let X be a Hilbert space and let Cn, n = 1, . . . ,N be convex closed subsets of X . The convex feasibility problem is to find some point x ∈ N ⋂ n=1 Cn, when this intersection is non-empty. In this talk we discuss projection algorithms for finding such a feasibility point. These algorithms have wide ranging applications including: solutions to convex inequalities, minimization of convex nonsmooth functions, medical imaging, computerized tomography, and electron microscopy Introduction and Outline Convex Feasibility Problems Convex Douglas–Rachford Non-Convex Douglas–Rachford Applications to Matrix Completion Abstract Let X be a Hilbert space and let Cn, n = 1, . . . ,N be convex closed subsets of X . The convex feasibility problem is to find some point x ∈ N ⋂Let X be a Hilbert space and let Cn, n = 1, . . . ,N be convex closed subsets of X . The convex feasibility problem is to find some point x ∈ N ⋂ n=1 Cn, when this intersection is non-empty. In this talk we discuss projection algorithms for finding such a feasibility point. These algorithms have wide ranging applications including: solutions to convex inequalities, minimization of convex nonsmooth functions, medical imaging, computerized tomography, and electron microscopy Introduction and Outline Convex Feasibility Problems Convex Douglas–Rachford Non-Convex Douglas–Rachford Applications to Matrix Completion