Scholarlink

<p>The main purpose of this paper is to extend the golden ratio algorithm for monotone mixed variational inequalities (Math Program 184(1):383–410, 2020) to solve a nonlinear inclusion problem that involves non-monotone and locally Lipschitz continuous operators. We show that the developed iterative sequence converges towards some solution of the nonlinear inclusion problem. Furthermore, our analysis reveals our algorithm owns the <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10915_2025_2903_Article_IEq1.gif" Format="GIF" Height="22" Rendition="HTML" Resolution="72" Type="Linedraw" Width="36" /> </InlineMediaObject> <EquationSource Format="TEX">\(O(\frac{1}{k})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>O</mi> <mo stretchy="false">(</mo> <mfrac> <mn>1</mn> <mi>k</mi> </mfrac> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> convergence rate and the linear convergence rate. In addition to inheriting all the benefits of the golden ratio algorithm from (Math Program 184(1):383–410, 2020), our algorithm has inertial accelerations and two types of self adaptive step sizes, when applied to monotone mixed variational inequalities.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

A New Golden Ratio Inertial Algorithm with Two Types of Self Adaptive Step Sizes for Solving Nonlinear Inclusion Problems

  • 期刊论文

  • 发表日期：

    2025年4月28日

查看全文
  • Zhong-bao Wang,
  • Xing-yu Chen,
  • Zhang-you Chen

摘要

The main purpose of this paper is to extend the golden ratio algorithm for monotone mixed variational inequalities (Math Program 184(1):383–410, 2020) to solve a nonlinear inclusion problem that involves non-monotone and locally Lipschitz continuous operators. We show that the developed iterative sequence converges towards some solution of the nonlinear inclusion problem. Furthermore, our analysis reveals our algorithm owns the \(O(\frac{1}{k})\) O ( 1 k ) convergence rate and the linear convergence rate. In addition to inheriting all the benefits of the golden ratio algorithm from (Math Program 184(1):383–410, 2020), our algorithm has inertial accelerations and two types of self adaptive step sizes, when applied to monotone mixed variational inequalities.