A strong convergence theorem for a general split equality problem with applications to optimization and equilibrium problem

Eslamian, Mohammad; Shehu, Yekini; Iyiola, Olaniyi S.

doi:10.1007/s10092-018-0290-3

Cited by 10 publications

(2 citation statements)

References 34 publications

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“…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. In addition, they presented a strong convergence theorem which is more desirable than weak convergence.…”

Section: Introductionmentioning

confidence: 99%

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Linear Convergence of Split Equality Common Null Point Problem with Application to Optimization Problem

2020

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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.

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Section: Introductionmentioning

confidence: 99%

“…In [10], it has been proved that the sequence {w n } generated by algorithm (8) converges strongly to a solution w * of the SECNP (3), and w * = P Γ (α) Γ is the solution set of SECNP (7) . However, as with most algorithms, the convergence rate of the iterative sequence (8) is not taken into account.…”

Section: Introductionmentioning

confidence: 99%

Linear Convergence of Split Equality Common Null Point Problem with Application to Optimization Problem

2020

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New Algorithms for Solving the Split Equality Problems in Hilbert Spaces

Ha,

Tuyen

2024

Acta Math Vietnam

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A strongly convergent algorithm for solving split equality problems beyond monotonicity

Mewomo,

Uzor,

Gibali

2024

Comp. Appl. Math.

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In this paper, we focus on some split inverse problems, namely the split equality variational inequalities and common fixed point problems, and combine various operator theory techniques to establish minimum-norm strong convergence for our proposed method. We present two strong convergent results with (and without) reference to the monotonicity property of the cost operators. Our convergence analyses assume very mild conditions and thus generalize and extend recent related results in the literature. Furthermore, several numerical examples illustrate the practical potentials and advantages of our proposed algorithm.

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A strong convergence theorem for a general split equality problem with applications to optimization and equilibrium problem

Cited by 10 publications

References 34 publications

Linear Convergence of Split Equality Common Null Point Problem with Application to Optimization Problem

Linear Convergence of Split Equality Common Null Point Problem with Application to Optimization Problem

New Algorithms for Solving the Split Equality Problems in Hilbert Spaces

A strongly convergent algorithm for solving split equality problems beyond monotonicity

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