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<p>In this article, we propose an improved viscosity algorithm for solving pseudomonotone equilibrium problems. A strong convergence theorem is established under certain conditions on the bifunction, along with suitable assumptions on the initial parameters and control sequences. We present two numerical examples, one in the finite-dimensional space <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math> <msup> <mi mathvariant="double-struck">R</mi> <mi>n</mi> </msup> </math></EquationSource> <EquationSource Format="TEX">$\mathbb{R}^{n}$</EquationSource> </InlineEquation> and the other in the infinite-dimensional space <InlineEquation ID="IEq2"> <EquationSource Format="MATHML"><math> <msup> <mi>ℓ</mi> <mn>2</mn> </msup> </math></EquationSource> <EquationSource Format="TEX">$\ell ^{2}$</EquationSource> </InlineEquation>, which demonstrate that the proposed algorithm exhibits superior computational performance compared to existing algorithms. Also, to validate the applicability of the proposed method, we applied it to a signal processing problem, confirming its effectiveness in practical scenarios.</p>

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An inertial viscosity algorithm for equilibrium problems with application to signal restoration

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年12月23日

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  • Sujitha Pushparaj,
  • Nathiya N,
  • Pulak Konar

摘要

In this article, we propose an improved viscosity algorithm for solving pseudomonotone equilibrium problems. A strong convergence theorem is established under certain conditions on the bifunction, along with suitable assumptions on the initial parameters and control sequences. We present two numerical examples, one in the finite-dimensional space R n $\mathbb{R}^{n}$ and the other in the infinite-dimensional space ℓ 2 $\ell ^{2}$ , which demonstrate that the proposed algorithm exhibits superior computational performance compared to existing algorithms. Also, to validate the applicability of the proposed method, we applied it to a signal processing problem, confirming its effectiveness in practical scenarios.