An inertial forward-backward algorithm for monotone inclusions
This work addresses optimization problems for researchers in mathematical optimization, offering an incremental improvement by extending acceleration techniques to a broader class of monotone inclusion problems.
The authors tackled the problem of finding a zero of the sum of two monotone operators, with one being co-coercive, by proposing an inertial forward-backward splitting algorithm. They proved convergence in Hilbert spaces and demonstrated faster convergence than existing methods in numerical results, while maintaining similar per-iteration computational costs.
In this paper, we propose an inertial forward backward splitting algorithm to compute a zero of the sum of two monotone operators, with one of the two operators being co-coercive. The algorithm is inspired by the accelerated gradient method of Nesterov, but can be applied to a much larger class of problems including convex-concave saddle point problems and general monotone inclusions. We prove convergence of the algorithm in a Hilbert space setting and show that several recently proposed first-order methods can be obtained as special cases of the general algorithm. Numerical results show that the proposed algorithm converges faster than existing methods, while keeping the computational cost of each iteration basically unchanged.