Title: A product space reformulation with reduced dimension

Speaker: Rubén Campoy (University of Valencia)

Date and Time: Wed Oct 13, 17:00 AEST (Register here for remote connection via Zoom)

Abstract:

The product space reformulation is a powerful trick when tackling monotone inclusions defined by finitely many operators with splitting algorithms. This technique constructs an equivalent two-operator problem, embedded in a product Hilbert space, that preserves computational tractability. Each operator in the original problem requires one dimension in the product space. In this talk, we propose a new reformulation with a reduction on the dimension of the outcoming product Hilbert space. We shall discuss the case of not necessarily convex feasibility problems. As an application, we obtain a new parallel variant of the Douglas-Rachford algorithm with a reduction in the number of variables. The computational advantage is illustrated through some numerical experiments.