Full Text: PDF
Volume 3, Issue 3, 31 December 2021, Pages 533-554
Abstract. In this paper, we study a monotone inclusion problem involving the mixtures of composite and parallel-sum type monotone operators with one of them being a cocoercive operator. Since the resolvent of the composite operator does not have a closed-form solution, the exact three-operator splitting algorithm could not be directly applied. As a result, it is meaningful to propose an effective iterative algorithm to solve this resolvent operator. Based on the primal-dual idea, we first solve the resolvent of the composite operators under suitable conditions. Furthermore, we present two iterative algorithms to solve the composite monotone inclusion problem, and prove their convergence based on the inexact three-operator splitting algorithm. As an application, a corresponding composite convex optimization problem is solved by two novel approaches. Finally, some numerical experiments are investigated on the image deblurring problems to demonstrate the efficiency of the proposed algorithms.
How to Cite this Article:
Chunxiang Zong, Yuchao Tang, Dual three-operator splitting algorithms for solving composite monotone inclusion with applications to convex minimization, J. Appl. Numer. Optim. 3 (2021), 533-554.