Abstract:
Projection methods can be used for solving a range of feasibility and optimisation problems. Whenever the constraints are represented as the intersection of closed (convex) sets with readily implementable projections onto each of these sets, a projection based algorithm can be employed to force the iterates towards the feasible set. Some versions of projection methods employ approximate projections; one can also consider under- and over-relaxed iterations (such as in the Douglas-Rachford method). In this talk I will focus on the convergence of projection methods. This includes a recent work on to De Pierro’s conjecture in collaboration with Roberto Cominetti and Andrew Williamson.