The Relations Between A Nonempty Closed Convex Set And Its Recession Cone

Our working space is R n. Convex cones are important in convex analysis just as subspaces are important in linear analysis. Many optimization can be translated into convex optimization, Convex cones are special convex sets. The number of cones are so many, such as normal cones, nuclear cones, preudonuclear cones etc. Recession cones which can be produced by a nonempty convex set are special cones. In this paper, we mainly study the relations between recession cones and a nonempty set. Some authors have considered and have got some quite good results. The main purpose of this paper is that by using the methods of former authors and the sufficient and necessary condition of cones, we do some relative deeply research for recession cones. Here, we get some results under certain constraint.The whole paper has four chapters altogether. The main part is the third chapter and fourth chapter. In the third chapter, we first introduce a new definition-pseudocone, then we talk over the relations between pseudocone and cone. Theorem 3.1 tells us the relations between recession cones and a nonempty close set. Finally, we give a sufficient and necessary condition to judge whether a recession cones are pointed cones and satisfy weak property (Ï€). In the fourth chapter, we first introduce the definition and property of general inequalities. Then we give some conditions for convex sets so they satisfy general inequalities about recession cones. At last we study linear inequalities related to dual cones in linear spaces.