r-凸函數在二階錐和n維實數空間上的一些結果

Abstract

Martos和Avriel獨立的定義一群實數函數，稱為r-凸函數，而且Avriel更進一步的研究它們。擬凸函數包含它們，而且它們包含凸函數。本篇論文給一些r-凸函數的例子，以及延伸r-凸函數和擬凸函數的概念到二階錐上。A family of real functions, called $r$-convex functions, were independently defined by Martos and Avriel and studied by the latter author. This family properly includes the family of convex functions and is included in the family of quasiconvex functions. This paper gives some examples of $r$-convex functions, extends the r-convexity and quasi-convexity concepts to the second-order cone.