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<p>The exact penalty function method is a commonly used unconstrained optimization technique for solving nonlinear optimization problems with constraints. Due to the complexity of interval-valued vector optimization problems, there are almost very few effective penalty functions to handle these problems. This paper aims at constructing an unconstrained interval-valued vector optimization problem related to a nondifferentiable interval-valued vector optimization problem via the exact <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(l_1\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>l</mi> <mn>1</mn> </msub> </math></EquationSource> </InlineEquation> penalty function. Under some suitable convexity assumptions, the equivalence of the (weakly) LU-efficient solution of the interval-valued vector original and the penalized optimization problem is proved. Moreover, we introduce a new interval-valued vector Lagrange function and analyze the relation between a (weakly) LU-efficient solution of the corresponding interval-valued vector penalized optimization problem and a saddle point of the defined Lagrange function. Some examples are given to illustrate the derived results.</p>

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An Exact \(l_1\) Penalty Function Method and Saddle Point Criteria for Interval-Valued Vector Optimization Problems

  • 期刊论文

  • 发表日期：

    2025年11月20日

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  • Huan Cheng,
  • Man-Xue You

摘要

The exact penalty function method is a commonly used unconstrained optimization technique for solving nonlinear optimization problems with constraints. Due to the complexity of interval-valued vector optimization problems, there are almost very few effective penalty functions to handle these problems. This paper aims at constructing an unconstrained interval-valued vector optimization problem related to a nondifferentiable interval-valued vector optimization problem via the exact \(l_1\) l 1 penalty function. Under some suitable convexity assumptions, the equivalence of the (weakly) LU-efficient solution of the interval-valued vector original and the penalized optimization problem is proved. Moreover, we introduce a new interval-valued vector Lagrange function and analyze the relation between a (weakly) LU-efficient solution of the corresponding interval-valued vector penalized optimization problem and a saddle point of the defined Lagrange function. Some examples are given to illustrate the derived results.