The Study Of Some Optimization Problems

This paper consists of three chapters.In the first chaper,we consider a classical inexact version for the proximal point algorithm generalized by Rockafellar for solving monotone inclusion problem.We obtain a new proof of the convergence,and it is simpler than the original one.In the second chapter,by introducing a new nonmonotone line search rule and combining it with quasi-Newton method,we propose a solution method for solving unconstranined optimzaition problems.Under mild conditions,we prove the global convergence of the second algorithm of this paper.In the third chapter,as an application of the inexact version for the Konnov projection method for solving varietional inequality problems,we analyze a solution method for the problem of the zero point of a operator which is continuous and satisfies a certain generalized monotonicity assumption in R~n,and we give the global convergence analysis.