Banach空间中的Lagrange乘子定理

摘要

In this paper, using the locally fine property for operators and the generalized preimage theorem, we extend the classical Lagrange multiplier theorem in Banach space. In particular, the constrained condition is really relaxed and the Lagrange multiplier λ is concretely represented in our theorem.%本文利用Banach空间中的局部精细概念和广义原像定理,拓宽了经典的Banach空间中的Lagrange乘子定理约束条件,特别地,将Lagrange乘子λ用泛函f在临界点的Frechét导数和约束g在该点的Frecchét导数的广义逆的乘积表示出来,即λ=f'(x).g'+(x).