Convergence of a Relaxed Inertial Forward–Backward Algorithm for Structured Monotone Inclusions

Inertial Krasnoselskii–Mann Method in Banach Spaces

“…Our Theorem 2 extends the results in [16,19,21,22,24,36] from Hilbert spaces to uniformly convex and q-uniformly smooth Banach spaces. 3.…”

“…Several other modifications of (2) with inertial extrapolation step have been considered in Hilbert spaces by many authors, see, for example, [17][18][19][20][21]. Based on the above mentioned results [19,[22][23][24][25][26], our main contribution in this paper is the following. We extend the results of [17] concerning the inertial Krasnoselskii-Mann iteration for fixed point of nonexpansive mappings to uniformly convex and q-uniformly smooth Banach space.…”

An inertial three-operator splitting algorithm with applications to image inpainting

“…We also presented numerical experiments on the constrained image inpainting problem (4.1) to demonstrate the advantage of introducing the inertial terms. We also find that the convergence of the iKM iteration (2.5) was discussed in [6,7] under certain conditions on the inertial parameters and the relaxation parameters, which are different from Lemma 2.2 and Lemma 2.3. It is natural to generalize the convergence analysis of the iKM iteration in [6,7] to the proposed inertial three-operator splitting algorithm.…”

“…We also find that the convergence of the iKM iteration (2.5) was discussed in [6,7] under certain conditions on the inertial parameters and the relaxation parameters, which are different from Lemma 2.2 and Lemma 2.3. It is natural to generalize the convergence analysis of the iKM iteration in [6,7] to the proposed inertial three-operator splitting algorithm. We would like to compare the performance of variants inertial threeoperator splitting algorithm for real world problems, and study the convergence rate analysis of the inertial three-operator splitting algorithm in the context of convex minimization in the future works.…”

Continuous Dynamics Related to Monotone Inclusions and Non-Smooth Optimization Problems

“…Making use of the the sequence (λ n ) n≥1 in (53), one obtains a relaxed forward-backward scheme, where the relaxation is usually considered in the literature in order to achieve more freedom in the choice of the parameters involved in the numerical scheme. We refer the reader to [12] where this fact has been underlined in the context of monotone inclusion problems.…”