无限凸优化问题的Lagrange对偶
Lagrange Duality of Infinite Convex Optimization
DOI: 10.12677/AAM.2026.159379, PDF,   
作者: 夏 爽：吉首大学数学与统计学院，湖南 吉首
关键词: 无限凸优化；强对偶；最优性条件；Infinite Convex Optimization； Strong Duality； Optimality Conditions
摘要: 借助共辄上图方法, 引入新的约束规范条件, 刻画了无线凸优化问题与对偶问题之间的 Lagrange 强对偶, 并推导出互补松弛条件与近似最优性条件, 推广了现有凸优化对偶相关结论.
Abstract: By virtue of the epigraph method of conjugates, this paper introduces new constraint qualification conditions, characterizes Lagrange strong duality between the infinite convex optimization problem and its dual problem, derives complementary slackness conditions and approximate optimality conditions, and generalizes the existing conclusions related to duality in convex optimization.
文章引用：夏爽. 无限凸优化问题的Lagrange对偶[J]. 应用数学进展, 2026, 15(9): 125-136. https://doi.org/10.12677/AAM.2026.159379

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