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<p>In this paper, we present an SQP-type proximal gradient method, named SQP-PG, for constrained composite optimization problems. To obtain a search direction at each iteration of SQP-PG, a subproblem should be solved. The optimal solution of the subproblem is computed by using the semismooth Newton method to solve the dual problem. We prove the global convergence of SQP-PG and analyze the iteration complexity for obtaining an <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40305_2025_634_Article_IEq2.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="11" /> </InlineMediaObject> <EquationSource Format="TEX">\(\varepsilon \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ε</mi> </math></EquationSource> </InlineEquation>-stationary point. Numerical results demonstrate that, compared to the state-of-the-art algorithms, SQP-PG is an efficient method and converges very fast.</p>

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An SQP-Type Proximal Gradient Method for Constrained Composite Optimization

  • 期刊论文

  • 发表日期：

    2025年9月22日

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  • Pin-Zheng Wei,
  • Wei-Hong Yang

摘要

In this paper, we present an SQP-type proximal gradient method, named SQP-PG, for constrained composite optimization problems. To obtain a search direction at each iteration of SQP-PG, a subproblem should be solved. The optimal solution of the subproblem is computed by using the semismooth Newton method to solve the dual problem. We prove the global convergence of SQP-PG and analyze the iteration complexity for obtaining an \(\varepsilon \) ε -stationary point. Numerical results demonstrate that, compared to the state-of-the-art algorithms, SQP-PG is an efficient method and converges very fast.