摘要
本文在Banach空间利用函数的Frechet可微性,研究了不等式约束和混合约束问题的最优性条件。利用η-凸性,Slatcr条件推广了不等式约束问题的最优性必要条件,同时利用η-凸性讨论了最优性充分条件以及Lagrange对偶问题,得出Lagrange对偶问题与原问题最优值相等的结论。也在Banach空间讨论了等式约束问题的二阶必要条件。
This paper presents the optimality conditions in inequality constrained and mixed constrained problems in Banach space by means of Frechet derivatives. From the η-convex-ity,Slater's condition,the nescessary optimality conditions are developed in inequality constrained minimization problems. The η-convexity is also used in discussing sufficient optimality conditions and the Lagrange dual problem. It is obtained that the extremal values are equal in the primal problem and the dual problem. This paper also discussed the necessary optimality conditions of second order in the equality constrained problems.
关键词
巴拿赫空间
非线性规划
必要条件
Frechet derivatives
η-convexity
Slater's condition
Banach space
dual problems
