Subdifferential Properties Of A Perturbed Minimal Time Function In Normed Spaces

In this thesis,we study the perturbed minimal time function in a normed space.It is widely used in the fields of optimal control,variational analysis and perturbed optimization.It covers the minimal time function and the perturbed distance function as special case.Firstly,based on the Ekeland’s variational principle and the theory of non-smooth analysis,the formulas of perturbed minimal time function and bilateral minimal time function are given.Secondly,the relationship among perturbed minimal time function,bilateral minimal time function and it’s corresponding lower semicontinuous function is established.Finally,the basic properties of ε-subdifferential and limit subdifferential are analyzed,and the formulas of ε-subdifferential and limit subdifferential are given.The formulas can be depicted by corresponding characterization of lower semicontinuous function and sublevel set of supporting function.our main results cover the result about the perturbation distance function and the minimal time function.