arXiv subjects

Jinjian Chen

Publications and source records attributed to Jinjian Chen.

2 recordsLinked to original sources

arXiv2022

Four-operator splitting algorithms for solving monotone inclusions

Monotone inclusions involving the sum of three maximally monotone operators or more have received much attention in recent years. In this paper, we propose three splitting algorithms for finding a zero of the sum of four monotone operators, which are two maximally monotone operators, one monotone Lipschitz operator, and one cocoercive operator. These three splitting algorithms are based on the forward-reflected-Douglas-Rachford splitting algorithm, backward-forward-reflected-backward splitting algorithm, and backward-reflected-forward-backward splitting algorithm, respectively. As applications, we apply the proposed algorithms to solve the monotone inclusions problem involving a finite sum of maximally monotone operators. Numerical results on the Projection on Minkowski sums of convex sets demonstrate the effectiveness of the proposed algorithms.

math.OC↗

arXiv2022

Forward-partial inverse-half-forward splitting algorithm for solving monotone inclusions

In this paper we provide a splitting algorithm for solving coupled monotone inclusions in a real Hilbert space involving the sum of a normal cone to a vector subspace, a maximally monotone, a monotone-Lipschitzian, and a cocoercive operator. The proposed method takes advantage of the intrinsic properties of each operator and generalizes the method of partial inverses and the forward-backward-half forward splitting, among other methods. At each iteration, our algorithm needs two computations of the Lipschitzian operator while the cocoercive operator is activated only once. By using product space techniques, we derive a method for solving a composite monotone primal-dual inclusions including linear operators and we apply it to solve constrained composite convex optimization problems. Finally, we apply our algorithm to a constrained total variation least-squares problem and we compare its performance with efficient methods in the literature.

math.OC↗