The recession cone and recession function are very important research objects in Convex Analysis. They have extensive applications in the optimization theory. Firstly, we study the properties of the recession cone and recession function. The positive homogeneity and subadditivity of recession function are mainly discussed. And the different methods are considered to prove these properties. Secondly, we discuss the unboundedness of the convex sets and convex functions by using recession cone and recession function.
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