The Type Of Entropy-like Interior Proximal Point Algorithms With The Applications

We in this thesis consider a class of convex programming problems subjected to nonnegative constraints, and study two types of interior proximal methods.These methods depend on some particular nonlinear distance function that replaces the usual quadratic proximal term,and the resulting points are always interior points.They can be applied to variational inequalities and monotone inclusions.This thesis consists of three chapters, and is organized as follow:In the first chapter,we briefly introduce the background of interior proximal point algorithm and its research progress,and gives some basic concepts and notation. In the second chapter, we add to the usual quadratic proximal point term on the based of an entropy-like first order homogeneous distance function,through selecting the different parameters to make the objective function has a faster decent rate, and extend to the polyhedra. By the characteristics of entropy-like distance function, we give an important property of the solution set. In the third chapter,we obtain some convergence results of an entropy-like second order homogeneous distance function that subjected to nonnegative constraints,and we give some examples of practical applications to further analysis.