【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。更多还原

【Abstract】 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.更多还原