| 魏俊林,游曼雪.DC复合优化问题的两种Fenchel对偶模型研究[J].井冈山大学自然版,2024,45(2):12-20 |
| DC复合优化问题的两种Fenchel对偶模型研究 |
| RESEARCH ON TWO FENCHEL DUAL MODELS FOR DC COMPOSITE OPTIMIZATION PROBLEMS |
| 投稿时间：2023-10-11 修订日期：2023-11-25 |
| DOI：10.3969/j.issn.1674-8085.2024.02.003 |
| 中文关键词: DC复合凸优化 c-共轭框架 Fenchel对偶 均匀凸函数 |
| 英文关键词: DC composite optimization c-conjugate scheme Fenchel duality evenly convex function |
| 基金项目:国家自然科学基金项目(12001438)； 西华师范大学校级项目(18Q059， 19B043) |
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| 中文摘要: |
| 本研究考虑的模型为无约束的DC复合凸优化问题。首先，利用扰动方法，c-共轭框架下的广义凸共轭定理及均匀凸（简称e-凸）技术，建立了DC复合优化问题的两种Fenchel对偶问题。其次，利用c-共轭函数的上图性质，给出了三个重要的集合。最后，在e-凸函数的假设下，刻画了两对原—对偶问题的强对偶性以及两者之间的等价关系。 |
| 英文摘要: |
| The model considered in this paper is an unconstrained DC composite convex optimization problem. Firstly, two Fenchel duality problems for DC composite optimization problems are established by using perturbation method, generalized convex conjugation theorem under c-conjugate scheme and evenly convex (e-convex, in brief) technique. Secondly, three important sets are given by using the properties of the epigraph of the c-conjugate function. Finally, the strong duality of two pairs of primal-dual problems and the equivalence between them are described under the assumption of e-convex function. |
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