不确定非光滑半无限多目标优化问题的最优性与对偶
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重庆师范大学

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国家重点研发计划项目(No.2023YFA1011302);国家自然科学基金面上项目(No.12171063);重庆市高校创新研究群体项目(No.CXQT20014);重庆英才计划“包干制”项目(No.cstc2022ycjh-bgzxm0114)


Optimality and Duality for Nonsmooth Semi-infinite Multi-objective Optimization Problems with Uncertainy
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Chongqing Normal University

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    摘要:

    研究一类不确定非光滑半无限多目标优化问题的最优性条件与对偶问题。首先,提出了严格广义凸性和\varepsilon-严格拟广义凸性的定义。其次,利用Clarke次微分,在\varepsilon-严格拟广义凸性条件下建立了\varepsilon-拟解的充分最优性条件。最后,在广义凸性条件和严格广义凸性条件下,分别建立了\varepsilon-拟弱解和\varepsilon-拟解的Wolfe型对偶,研究了弱对偶、强对偶及逆对偶定理。所得结果完善了不确定非光滑半无限多目标优化问题的相关理论。

    Abstract:

    This study examines optimality conditions and dual problems for a category of uncertain nonsmooth semi-infinite multi-objective optimization issues. Initially, the definitions of the strictly generalized convexity and the strictly \varepsilon-quasi generalized convexity are presented. Secondly, the sufficient optimality condition for the \varepsilon-quasi solution is established under the strictly \varepsilon-quasi generalized convexity conditions utilizing the Clarke subdifferential. Finally, Wolfe-type dual problems of \varepsilon-quasi weak and \varepsilon-quasi solutions are established under the generalized convexity and strictly generalized convexity conditions, respectively, weak dual theorem, strong dual theorem and converse dual theorem are studied. The results acquired enhance the theory concerning uncertain nonsmooth semi-infinite multi-objective optimization issues.

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  • 收稿日期:2024-07-12
  • 最后修改日期:2024-10-30
  • 录用日期:2025-04-27
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