DC 型均匀凸优化问题的最优性条件和全对偶
Optimality Conditons and Total Dualities for DC Type Evenly Convex Optimization Problems
DOI: 10.12677/AAM.2025.145228, PDF,   
作者: 陈泓烨：吉首大学数学与统计学院，湖南 吉首
关键词: 均匀凸优化问题；最优性条件；全对偶；Evenly Vonvex Optimization Problem； Optimality Condition； Total Duality
摘要: 利用c-次微分概念，引入新的约束规范条件，给出了带DC型不等式的均匀凸优化问题的最优性条 件，同时利用均匀凸函数的性质，定义了原问题的Lagrange对偶问题，利用函数的c-共轭上图性 质，刻画了原问题与其Lagrange对偶问题之间的全对偶。
Abstract: By using the concept of c-subdifferential and introducing new constraint qualification-s, the optimality conditions for evenly convex optimization problems with DC type inequalities are given. At the same time, the Lagrange dual problem of the prime problem is defined by utilizing the properties of evenly convex functions. By utilizing the c-conjugate graph property of functions, the total dual problem between the prime problem and its Lagrange dual problem is depicted.
文章引用：陈泓烨. DC 型均匀凸优化问题的最优性条件和全对偶[J]. 应用数学进展, 2025, 14(5): 9-22. https://doi.org/10.12677/AAM.2025.145228

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