Maximal Monotone Operator And Self-dual Convex Functional In Non-reflexive Spaces

In this paper the main work is about the relationship between the self-dual lagrangian convex functions and maximal monotone operators within the non-reflexive space. The whole paper consists of three chapters.In the first chapter, to begin by introducing convex analysis, monotone operators and variational method, and their development, main content, dominating figure, lead to the pap-er’s research background and contents.In the second chapter, the main work is the variational method in non-reflexive space about the self-dual lagrangian convex functions. We begin from the existence of the lower semi-continuous convex functional extremum in the reflexive spaces, and generalize to the non-reflexive spaces. Using the weak star lower semi-continuous’characteristic, or the weak star lower semi-continuous from above property of convex functional in the non-reflexive spaces, we draw some conclusion. And we put these results apply to the lagrangian convex functional, drawing that the lagrangian convex functional also have the self-dual property and related proposition.In the third chapter, we study the relationship between the self-dual lagrangian convex functions and maximal monotone operators within non-reflexive spaces. Drawing a conclusion that self-dual lagrangian functions are maximal monotone operators and maximal monotone operators are self-dual vector in non-reflexive space.