Research On Interior Point Trust Region Algorithms For Nonlinear Optimization Problems

Nonlinear problem is an important part of optimization research,which has many applications in management,information science,economics,agricultural science and industrial engineering.In this paper,we studied the nonlinear optimization problems with constraints,and proposed the non-convex separable interior point trust region algorithm and affine interior point trust region algorithm for the two kinds of constrained optimization problems,which mainly included the following contents:Firstly,some basic conditions of the nonlinear constraint problem are introduced,including the concept and research method of the nonlinear constraint problem.In addition,the interior point trust region optimization algorithm is introduced,and the research content of this paper is given.Separable optimization problems are widely used in image processing,machine learning,etc.In this paper,we consider the inner point trust region algorithm for non-convex separable nonlinear constraint problems,and give the convergence properties of the inner point trust region algorithm.Different from the classical interior-point trust region method,we get the expression of the relaxation variable in the inequality constraint.Based on the expression of relaxation variables,an equivalent system for the logarithmic barrier problem is derived.Relevant numerical experiments show that the interior point trust region algorithm has fast convergence speed and good numerical performance.Finally,we study the nonlinear constrained optimization problem with bounded constraints,and propose and analyze an affine inner-point trust region method based on filter technique to solve the nonlinear optimization problem with bounded variables.Compared with the traditional method using penalty function,the filter technique is used to test the effect of iteration step,and the convergence of the inner point trust region algorithm is proved,and a numerical example is given.Finally,the thesis is summarized and further research directions are proposed.