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<p>This paper introduces a new golden ratio-type algorithm with nonmonotone and adaptive stepsize rule for approximating solutions of pseudo-monotone variational inequalities in Hilbert spaces. With appropriate choices of the control parameters, the proposed method naturally reduces to several new and computationally efficient golden-ratio-type algorithms. We establish strong convergence results for the sequence generated by our algorithm under standard assumptions. The theoretical analysis is validated through numerical experiments, including an academic example on the classical Hilbert space <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(L_2([0,1])\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>L</mi> <mn>2</mn> </msub> <mrow> <mo stretchy="false">(</mo> <mrow> <mo stretchy="false">[</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo stretchy="false">]</mo> </mrow> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> and practical applications in compressed sensing and image restoration problems Overall, the comparative numerical results against existing golden-ratio algorithms highlight the competitiveness and strong potential of the proposed algorithm.</p>

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Strongly convergent golden ratio algorithm for pseudomonotone variational inequalities with applications

  • 期刊论文

  • 发表日期：

    2026年7月22日

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  • Jian-Wen Peng,
  • Li Han,
  • Abubakar Adamu,
  • Jen-Chih Yao

摘要

This paper introduces a new golden ratio-type algorithm with nonmonotone and adaptive stepsize rule for approximating solutions of pseudo-monotone variational inequalities in Hilbert spaces. With appropriate choices of the control parameters, the proposed method naturally reduces to several new and computationally efficient golden-ratio-type algorithms. We establish strong convergence results for the sequence generated by our algorithm under standard assumptions. The theoretical analysis is validated through numerical experiments, including an academic example on the classical Hilbert space \(L_2([0,1])\) L 2 ( [ 0 , 1 ] ) and practical applications in compressed sensing and image restoration problems Overall, the comparative numerical results against existing golden-ratio algorithms highlight the competitiveness and strong potential of the proposed algorithm.