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<p>In this article, robust optimality for nonsmooth multiobjective programming problems and some remarks on Mond–Weir-type duality involving image space analysis (ISA) are employed. First, we study robust optimality conditions via a separation scheme for nonsmooth multiobjective optimization problems under data uncertainty (for brevity, (<InternalRef RefID="Equ1">UP</InternalRef>)) and discuss some fundamental characterizations for a class of regular weak separation functions as well as ISA. Second, in terms of augmented Lagrangian functions and image space analysis, we derive robust necessary and sufficient optimality conditions for the uncertain multiobjective programming problem. Finally, we shall show that the Mond–Weir-type duality is a Lagrange-type duality, addressing an interesting question that had been raised earlier in another related research paper under suitable assumptions on the <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathcal {C}-\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="script">C</mi> <mo>-</mo> </mrow> </math></EquationSource> </InlineEquation>differentiation of the objective and constraint functions. Some illustrative examples to demonstrate the obtained main results are provided, too.</p>

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An Image Space Analysis Approach for Nonsmooth Multiobjective Programming Problems Under Data Uncertainty

  • 期刊论文

  • 发表日期：

    2026年8月5日

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  • Tran Van Su,
  • Dinh Dieu Hang

摘要

In this article, robust optimality for nonsmooth multiobjective programming problems and some remarks on Mond–Weir-type duality involving image space analysis (ISA) are employed. First, we study robust optimality conditions via a separation scheme for nonsmooth multiobjective optimization problems under data uncertainty (for brevity, (UP)) and discuss some fundamental characterizations for a class of regular weak separation functions as well as ISA. Second, in terms of augmented Lagrangian functions and image space analysis, we derive robust necessary and sufficient optimality conditions for the uncertain multiobjective programming problem. Finally, we shall show that the Mond–Weir-type duality is a Lagrange-type duality, addressing an interesting question that had been raised earlier in another related research paper under suitable assumptions on the \(\mathcal {C}-\) C - differentiation of the objective and constraint functions. Some illustrative examples to demonstrate the obtained main results are provided, too.