Complexity of the relaxed Peaceman-Rachford splitting method for the sum of two maximal strongly monotone operators
نویسندگان
چکیده
This paper considers the relaxed Peaceman-Rachford (PR) splitting method for finding an approximate solution of a monotone inclusion whose underlying operator consists of the sum of two maximal strongly monotone operators. Using general results obtained in the setting of a non-Euclidean hybrid proximal extragradient framework, convergence of the iterates, as well as pointwise and ergodic convergence rate, are established for the above method whenever an associated relaxation parameter is within a certain interval. An example is also discussed to demonstrate that the iterates may not converge when the relaxation parameter is outside this interval.
منابع مشابه
Relatively Relaxed Proximal Point Algorithms for Generalized Maximal Monotone Mappings and Douglas-Rachford Splitting Methods
The theory of maximal set-valued monotone mappings provide a powerful framework to the study of convex programming and variational inequalities. Based on the notion of relatively maximal relaxed monotonicity, the approximation solvability of a general class of inclusion problems is discussed, while generalizing most of investigations on weak convergence using the proximal point algorithm in a r...
متن کاملIterative construction of the resolvent of a sum of maximal monotone operators
We propose two inexact parallel splitting algorithms for computing the resolvent of a weighted sum of maximal monotone operators in a Hilbert space and show their strong convergence. We start by establishing new results on the asymptotic behavior of the Douglas-Rachford splitting algorithm for the sum of two operators. These results serve as a basis for the first algorithm. The second algorithm...
متن کاملFaster Convergence Rates of Relaxed Peaceman-Rachford and ADMM Under Regularity Assumptions
Splitting schemes are a class of powerful algorithms that solve complicated monotone inclusion and convex optimization problems that are built from many simpler pieces. They give rise to algorithms in which the simple pieces of the decomposition are processed individually. This leads to easily implementable and highly parallelizable algorithms, which often obtain nearly state-of-the-art perform...
متن کاملThe sum of two maximal monotone operator is of type FPV
In this paper, we studied maximal monotonicity of type FPV for sum of two maximal monotone operators of type FPV and the obtained results improve and complete the corresponding results of this filed.
متن کاملA Forward-Backward Projection Algorithm for Approximating of the Zero of the Sum of Two Operators
In this paper, a forward-backward projection algorithm is considered for finding zero points of the sum of two operators in Hilbert spaces. The sequence generated by algorithm converges strongly to the zero point of the sum of an $alpha$-inverse strongly monotone operator and a maximal monotone operator. We apply the result for solving the variational inequality problem, fixed po...
متن کامل