摘要
系统研究了Hilbert空间L^2(Ω)上凸的半无限规划问题,推广了原问题与对偶问题最优解存在的充要条件。在非光滑的条件下,给出了正则条件的另一种表现形式,以及原问题与对偶问题无间隙的充分条件及Lagrange乘子集非空有界的充要条件。进而在光滑的条件下,给出了与Robinson条件等价的更一般的正则条件以及减弱对约束函数的限制条件。该结论丰富和发展了半无限规划理论。
The convex semi-infinite programming problem on Hilbert space was investigated systematically,with the sufficient and necessary conditions for the existence of optimal solutions of the prime and dual problems generalized.Another form of regular condition was proposed in the case of nonsmooth problem,with the sufficient and necessary conditions for the no-gap of the prime and dual problems and the non-empty bounded of the Lagrange multiplier set given.Moreover,a general regularization condition equivalent to Robinson’s condition in the case of smooth problem and a weakening restriction condition for constraint function are presented.The results enrich and develop the theories and applications foundation of semi-infinite programming.
作者
马欣荣
高智锴
段治健
MA Xinrong;GAO Zhikai;DUAN Zhijian(School of Mathematics and Information Science,Xianyang Normal University,Xianyang 712000,Shaanxi,China)
出处
《咸阳师范学院学报》
2019年第4期5-8,共4页
Journal of Xianyang Normal University
基金
陕西省教育科学“十三五”规划课题（SGH18H356）
航空科学基金项目（2017ZA53001）
陕西省大学生创新创业训练计划项目（S201910722040）
关键词
凸的
半无限规划
对偶问题
最优解
Lagrange乘子集
convex
semi-infinite programming
the duality problem
optimal solutions
Lagrange multiplier set
