Generalized Convexity of Lower Semicontinuous Functions and Generalized Monotonicity of their Subdifferentials

Abstract

本文主要考虑下半连续函数的广义凸性及其次微分算子的广义单调性之间的关系。 我们分别利用下半连续函数的Fr\'{e}chet~$\epsilon$-次微分、 KM~$\epsilon$-次微分和KM次微分给出相应函数拟凸的一个等价刻画，并证明了下 半连续函数的拟凸性与其相应的三种次微分算子的拟单调性之间的等价性。我们还得到一个拟凸和 伪凸之间的关系，以及函数伪凸与其Fr\'{e}chet~$\epsilon$-次微分算子伪单调之间的关系。This dissertation mainly considers the relationship between generalized convexity of lower semicontinuous functions and generalized monotonicity of their subdifferentials. In particular, we characterize the quasi-convexity of a lower semicontinuous function respectively by its Fr\'{e}chet~$\epsilon$-subdifferential, KM~$\epsilon$-subdifferential and KM subdifferential, and then prove the equ...学位：理学硕士院系专业：数学科学学院数学与应用数学系_基础数学学号：1912008115272