β-光滑Banach空间中一类数学规划问题的最优必要条件

Necessary Conditions for a Kind of Constrained Optimization Problems in β-Smooth Banach Spaces

在一般 Banach空间中 ,提出数学规划问题的偏静态条件定义 ,在目标函数和约束函数均为扩张值下半连续函数的情形下 ,获得了罚问题解的一个结果 ,该结果改进和推广了已有的相应结果 ,并由此证明了β-光滑 Banach空间中的模糊乘子规则 ,从而找出该类数学规划问题的最优必要条件 .

This paper gives a definition of partial calmnessof constrained optimization problems and verifies an important result under con ditons of the lower semicontinuties for objective function and other constrainedfunctions in Banach spaces. Then we use the results to prove a fuzzy miltiplierrule of optimizaiton problems which have lower semicontinuous objective functio n and lower semicontinuous constrained functions in β-Smooth Banach Spaces. The rule is a necessary condition for constrained optimization problems.