604. Regularized splitting method for three operators inclusion problems of “two maximal monotone + one cocoercive” and its applications
Invited abstract in session MC-50: Splitting algorithms, stream Variational analysis, equilibria and nonsmooth optimization.
Monday, 12:30-14:00Room: Parkinson B11
Authors (first author is the speaker)
| 1. | Xingju Cai
|
| Nanjing Normal University |
Abstract
This paper considers finding a zero point of A + B + C, where A and C are maximal monotone and B is ξ-cocoercive. The three-operator splitting method, proposed by Davis and Yin, is a popular algorithm for solving this problem. Observing that the x-sequence and the y-sequence in Davis-Yin method have the same accumulation point and B’s information is only utilized in the second subproblem, this work proposes a new splitting method named the regularized splitting method (RSM), where “x = y” is introduced as a penalty term and the forward step is also employed in the first subproblem. The penalty term can balance the differences between the two subproblems and the additional forward step enables utilizing B’s information in both subproblems simultaneously. We establish the convergence of the proposed method and demonstrate its sublinear convergence rate concerning the fixed-point residuals, assuming mild conditions in an infinite dimensional Hilbert space. This approach not only generalizes the Douglas-Rachford splitting method and Davis-Yin method, but also, to our knowledge, uniquely correlates with the symmetric alternating direction method of multipliers–a correspondence that is absent in current maximal monotone operator splitting algorithms. We also give some application of this method.
Keywords
- Continuous Optimization
- Programming, Nonlinear
- Convex Optimization
Status: accepted
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