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<p>In this paper, we propose a nonmonotone line search method for solving nonlinear constrained optimization problems, without the use of any penalty functions or filters. The algorithm generates an iteration sequence that is divided into three types: the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(f-\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>f</mi> <mo>-</mo> </mrow> </math></EquationSource> </InlineEquation>type for improving optimality, the <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(c-\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>c</mi> <mo>-</mo> </mrow> </math></EquationSource> </InlineEquation>type for enhancing feasibility and the <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(v-\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>v</mi> <mo>-</mo> </mrow> </math></EquationSource> </InlineEquation>type as a relaxed criterion for avoiding the Maratos effect. A penalty-free acceptance criterion is employed to ensure global convergence. Under mild conditions, the algorithm achieves superlinear convergence without the need for second order corrections or a feasibility restoration phase. Furthermore, we present numerical results for a set of constrained problems from the CUTEr collection.</p>

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A penalty-free method with nonmonotone line search for nonlinear optimization

  • 期刊论文

  • 发表日期：

    2025年11月20日

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  • Ting Xu,
  • Qi Zhao,
  • Wenhao Fu,
  • Zhongwen Chen

摘要

In this paper, we propose a nonmonotone line search method for solving nonlinear constrained optimization problems, without the use of any penalty functions or filters. The algorithm generates an iteration sequence that is divided into three types: the \(f-\) f - type for improving optimality, the \(c-\) c - type for enhancing feasibility and the \(v-\) v - type as a relaxed criterion for avoiding the Maratos effect. A penalty-free acceptance criterion is employed to ensure global convergence. Under mild conditions, the algorithm achieves superlinear convergence without the need for second order corrections or a feasibility restoration phase. Furthermore, we present numerical results for a set of constrained problems from the CUTEr collection.