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5. 利用Greenberg-Pierskalla次微分研究半无限拟凸规划的Karush-Kuhn-Tucker条件

利用Greenberg-Pierskalla次微分研究半无限拟凸规划的Karush-Kuhn-Tucker条件

来源 :西华师范大学学报（自然科学版） | 被引量 : 0次 | 上传用户：YX19781987

【摘 要】

：

最优性条件是最优化理论的一个重要研究方向,为优化算法的研究提供了重要的理论基础,且近几十年来在凸规划中已经获得丰富的理论成果.然而,拟凸函数的性质导致KKT条件在拟凸规划中很少被表示,尤其是半无限情形.考虑半无限拟凸规划,利用Greenberg-Pierskalla次微分的并集的凸包来刻画约束集的法锥,得到相应的KKT充分必要条件.本文定理4和5将文献[1]中定理5拓展到半无限拟凸规划.最后将本文定理5应用到半无限凸规划情形.

【作 者】

：

赵丹 田倍昕 游曼雪 

【机 构】

：

西华师范大学 数学与信息学院,四川 南充 637009

【出 处】

：

西华师范大学学报（自然科学版）

【发表日期】

：

2021年4期

【关键词】

：

半无限规划 KKT充要条件 Greenberg-Pierskalla次微分 本质拟凸 Slater约束规范 

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论文部分内容阅读

最优性条件是最优化理论的一个重要研究方向,为优化算法的研究提供了重要的理论基础,且近几十年来在凸规划中已经获得丰富的理论成果.然而,拟凸函数的性质导致KKT条件在拟凸规划中很少被表示,尤其是半无限情形.考虑半无限拟凸规划,利用Greenberg-Pierskalla次微分的并集的凸包来刻画约束集的法锥,得到相应的KKT充分必要条件.本文定理4和5将文献[1]中定理5拓展到半无限拟凸规划.最后将本文定理5应用到半无限凸规划情形.

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