Hilbert空间上非凸函数的共轭函数与极值

CONJUGATE FUNCTION AND EXTREMA OF NONCONVEX FUNCTION IN HILBERT SPACE

在Hilbert空间上对非凸函数,引进了共轭函数的概念并讨论了共轭函数的若干性质及与闭包函数之间的关系。利用共轭函数和闭包函数刻划了问题(P)的一些最优性条件。这里, (P) min f(x)f:H→(+∞,-∞〕为任一函数,H为—Hilbert空间。

The concept of conjugate function of nonconvex function is introduced in Hilbert space,and some properties of conjugate function and its relationship with closure function are discussed, and several optimal conditions of problem (P) are obtained on the basis of conjugate function and closure function, where (P) min f(x) x∈H f:H →( - ∞, +∞] is any function,H is a Hilbert space.