Research On The Properties Of Augmented Lagrangian Function In Cone Constrained Optimization

Optimization problems are widely used in national defense economy, finance, en-gineering and other important fields. Cone constraint problem is a very important optimization problem. It contains nonlinear programming, semidefinite program-ming and semiinfinite programming and so on. In this paper, we study the aug-mented Lagrangian function of cone programming and analyze the necessary and sufficient conditions for the existences of the augmented Lagrangian multipliers, and the corresponding results are given in some special cases. This paper is divided into three chapters:In chapter one, we mainly introduce the research background and research situation.In chapter two, we generalize and improve the results of Zhou[12]. A necessary and sufficient condition for the existence of the augmented Lagrangian multipliers is given. On the basis of this, some sufficient conditions for the existence of multipliers are given. Compared with [12], two sufficient conditions for the existence of the augmenting Lagrangian multipliers that don't need augmenting functions meet the growth conditions.In chapter three, we define a class of more general nonlinear augmented La-grangian. Based on those functions, we deal with the relationship among the exis-tence of global saddle points, augmented Lagrangian multipliers and zero duality gap property. Further we give the necessary and sufficient conditions for the existence for nonlinear augmented Lagrangian multipliers. We establish the nonlinear aug-mented Lagrangian function can cover most of the augmented Lagrangian function form. Therefore, this conclusion is more generality.