基于广义共轭的约束优化问题推广的Farkas引理及Lagrange对偶
Generalized Farkas’ Lemma and Lagrange Duality for Constrained Optimization Problems Based on Generalized Conjugacy
DOI: 10.12677/aam.2025.147364, PDF,   
作者: 吴柯幸：吉首大学数学与统计学院，湖南 吉首
关键词: C-共轭；Farkas引理；强对偶；C-Conjugate； Farkas’ Lemma； Strong Duality
摘要: 利用广义共轭上图性质，引入新的约束规范条件，等价刻画了约束优化问题推广的Farkas引理。然后，定义了基于广义共轭的Lagrange对偶问题，建立了约束优化问题与其对偶问题之间的Lagrange强对偶及稳定强对偶，推广和改进了前人的相关结论。
Abstract: By utilizing the properties of generalized conjugate upper graphs and introducing new constraint qualification conditions, the generalized Farkas lemma for constrained optimization problems is equivalently characterized. Then, the Lagrange dual problem based on generalized conjugates is defined, and the Lagrange strong duality and stable strong duality between the constrained optimization problem and its dual problem are established, which generalizes and improves the relevant conclusions of predecessors.
文章引用：吴柯幸. 基于广义共轭的约束优化问题推广的Farkas引理及Lagrange对偶[J]. 应用数学进展, 2025, 14(7): 284-292. https://doi.org/10.12677/aam.2025.147364

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