回收锥和回收函数的性质

The Properties of Recession Cone and Recession Function

回收锥和回收函数作为凸分析的重要研究对象,在最优化理论中有着广泛的应用。本文首先根据渐近锥和回收锥有关交集运算的性质推导出了渐近锥关于并集运算的性质。其次,针对正则条件下回收函数的四则运算进行了讨论,并得出了相应的结论。最后,举例说明了回收函数一些性质成立时相关条件的合理性。

The recession cone and recession function are extremely important research objects in Convex Analysis. They have extensive applications in the optimization theory. Firstly, this article investigates the properties of union operation of asymptotic cones based on the properties of the intersection operation of asymptotic cone and recession cone. Secondly, the four operations of the recession function under regular conditions are discussed and corresponding conclusions are drawn. Finally, examples are given to illustrate the rationality of the relevant conditions when some properties of recession function hold.