A new extragradient algorithm with adaptive step-size for solving split equilibrium problems
He (J. Inequal. Appl. 2012:Article ID 162 2012 ) introduced the proximal point CQ algorithm (PPCQ) for solving the split equilibrium problem (SEP). However, the PPCQ converges weakly to a solution of the SEP and is restricted to monotone bifunctions. In addition, the step-size used in the PPCQ is a...
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Published in | Journal of inequalities and applications Vol. 2021; no. 1; pp. 1 - 14 |
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Main Authors | , , , |
Format | Journal Article |
Language | English |
Published |
Cham
Springer International Publishing
02.08.2021
Springer Nature B.V SpringerOpen |
Subjects | |
Online Access | Get full text |
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Summary: | He (J. Inequal. Appl. 2012:Article ID 162
2012
) introduced the proximal point CQ algorithm (PPCQ) for solving the split equilibrium problem (SEP). However, the PPCQ converges weakly to a solution of the SEP and is restricted to monotone bifunctions. In addition, the step-size used in the PPCQ is a fixed constant
μ
in the interval
(
0
,
1
∥
A
∥
2
)
. This often leads to excessive numerical computation in each iteration, which may affect the applicability of the PPCQ. In order to overcome these intrinsic drawbacks, we propose a robust step-size
{
μ
n
}
n
=
1
∞
which does not require computation of
∥
A
∥
and apply the adaptive step-size rule on
{
μ
n
}
n
=
1
∞
in such a way that it adjusts itself in accordance with the movement of associated components of the algorithm in each iteration. Then, we introduce a self-adaptive extragradient-CQ algorithm (SECQ) for solving the SEP and prove that our proposed SECQ converges strongly to a solution of the SEP with more general pseudomonotone equilibrium bifunctions. Finally, we present a preliminary numerical test to demonstrate that our SECQ outperforms the PPCQ. |
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ISSN: | 1029-242X 1025-5834 1029-242X |
DOI: | 10.1186/s13660-021-02668-x |