Given a Hilbert space and a finite family of operators defined on the space, the common fixed point problem (CFPP) is the problem of finding a point in the intersection of the fixed point sets of these operators. A particular case of the problem, when the operators are orthogonal projections, is the convex feasibility problem … Read more
We propose new primal-dual decomposition algorithms for solving systems of inclusions involving sums of linearly composed maximally monotone operators. The principal innovation in these algorithms is that they are block-iterative in the sense that, at each iteration, only a subset of the monotone operators needs to be processed, as opposed to all operators as in … Read more
A definition of oblique projections onto closed convex sets that use seminorms induced by diagonal matrices which may have zeros on the diagonal is introduced. Existence and uniqueness of such projections are secured via directional affinity of the sets with respect to the diagonal matrices involved. A block-iterative algorithmic scheme for solving the convex feasibility … Read more