Danskin's Theorem Statement 1 假设ϕ(x,z)ϕ(x,z)为含有两个变量的连续函数:ϕ:Rn×Z→Rϕ:Rn×Z→R,其中Z⊂RmZ⊂Rm为紧集。 进一步假设,对于任意z∈Zz∈Z,ϕ(x,z)ϕ(x,z)是关于xx的凸函数。 在这两个条件下,Danskin 定理给出了关于函数f(x)=maxz∈Zϕ(x,z)f(x)=maxz∈...
(College0fMath~naticsandInformaticsScience,$hawdNormalUnlvemty,)(i' ∞ 710062.China) Abstract:Inthispaper,weprovethatacorrectedformoftheDamkintheoremondirectionalder ivativeholdsundera weakercondition. Keywords:pretopologicalspace;sequentialcompactness;continuous;directionalderivativ e (责任编辑:王金莲)...
In this appendix we state and prove a theorem due to Danskin, which was used in Chapter 5, in the proof of Theorem 5.1. We also show how this result applies to prove a stronger version of Theorem 5.1, under weaker hypotheses (than those given in Chapter 5)....
patterntheorem. Kestenoriginallyappliedhispatterntheoremtoprovethefollowing ratiolimittheorems: limCN+2 Jl2, (7.1.1) = N-ooCN r q2N+2 Jl2, (7.1.2) tm--= N-ooq2N limbN+t=Jl· (7.1.3) N-oo--;;;:;- WeshallprovetheseresultsinSection7.3.Unfortunately,thesamemeth- ...
In this appendix we state and prove a theorem due to Danskin, which was used in Chapter 5, in the proof of Theorem 5.1. As far as we know, the original version was first presented in [33]. Since then, many more general forms have been derived. More discussion on this can be found...
In this appendix we state and prove a theorem due to Danskin, which was used in Chapter 5, in the proof of Theorem 5.1. As far as we know, the original version was first presented in [33]. Since then, many more general forms have been derived. More discussion on this can be found...