Study On Second Order Strict Minimal Points In Hilbert Space

Strict minimum is an important concept in mathematical planning and optimization,and second-order strict minimum has played an important role in mathematical planning.On the basis of work in the finite dimension space,this article mainly studies second-order minimum of a given nonsmooth function defined on the Hilbert space.This paper first introduces the definition and properties of the second-order Dini-direction derivative.By applying the above results and the Necessity and sufficiency of the second order strict minima in finite dimensional space,we mainly study the problem of the Second Order Hilbert space,and give the necessary and sufficient conditions to guarantee the second order exact minimum.This paper extends the study of second order exact minimum points from finite dimensional space to Hilbert space.