Abstract
The purpose of this paper is to propose an iterative algorithm for solving the split equality common null point problem (SECNP), which is to find an element of the set of common zero points for a finite family of maximal monotone operators in Hilbert spaces. We introduce the concept of bounded linear regularity for the SECNP and construct several sufficient conditions to ensure the linear convergence of the algorithm. Moreover, some numerical experiments are given to test the validity of our results.
Highlights
Let H1, H2, H3 be real Hilbert spaces, C and Q be nonempty closed convex subsets of H1 and H2, respectively
Reduces to the split feasibility problem (SFP) which was introduced by Censor and Elfving [2]
Eslamian [10] considered an algorithm for solving split equality common null point problem (SECNP) for a finite family of maximal monotone operators which does not require any knowledge of the operator norms
Summary
Let H1 , H2 , H3 be real Hilbert spaces, C and Q be nonempty closed convex subsets of H1 and H2 , respectively. In [7], Moudafi introduced and studied the following split equality null point problem (SENP): given two set-valued maximal monotone operators F : H1 → 2 H1 and K : H2 → 2 H2 , the SENP is formulated as finding x ∗ ∈ F −1 (0), y∗ ∈ K −1 (0) such that Ax ∗ = By∗ ,. To implement the alternating algorithm (4) for solving SENP (2), we need to compute k Ak and k Bk, which is generally not an easy task in practice To overcome this difficulty, Eslamian [10] considered an algorithm for solving SECNP for a finite family of maximal monotone operators which does not require any knowledge of the operator norms.
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