回收锥与回收函数的若干性质

Some properties of recovery cone and recovery function

首先,研究了回收函数的性质,得到了线性条件下回收函数满足正齐次性和次可加性;其次,通过举例说明若函数不具备线性条件,则回收函数不一定满足正齐次性和次可加性;最后,给出了回收锥在线性变化下的性质,同时,若将凸性条件弱化为近似凸时,其闭包的回收锥和相对内部的回收锥仍然相等,并通过举例说明了合理性。

This paper studies some properties of the recovery cone and recovery function.First,the properties of the recovery function are studied,and the recovery function satisfies positive homogeneity and subadditivity under linear conditions.Secondly,through an example,if the function does not have linearity,the recovery function does not necessarily satisfy positive homogeneity and subadditivity.Finally,the properties of the recovery cone under linear change are given.At the same time,if the convexity condition is weakened to approximately convex,the recovery cone of the closure and the relatively inner recovery cone are still equal,and the rationality is illustrated by examples.