Research On Smoothing Algorithm For Systems Of Nonlinear Equalities And Inequalities

The systems of equalities and inequalities in data analysis,set separation,image restoration and other problems have very important applications.The solving methods of linear equalities and inequalities systems have been relatively mature.For nonlinear equalities and inequalities systems,although there are a lot of research results,but they have their own advantages and disadvantages,there are a lot of content are worth studying.In this paper,the study is presented to solve nonlinear equalities and inequalities systems,the research contents are as follows:(1)For the system of nonlinear inequalities,this paper smoothing function is improved,the smoothing function instead of a two-stage function,with the thought of smoothing refactoring,by using the smoothing function,the inequalities system is transformed into smoothing equations with smoothing parameters,with smoothing Newton algorithm for its solution,and finally prove that under certain assumptions the well-posedness of the algorithm,and the convergence of the algorithm.Numerical experiments show that the algorithm is feasible.(2)On the basis of inequalities system,the smoothing method is applied to solving the general systems of equalities and inequalities.Also use smoothing reconstruction of ideas,the equalities and inequalities systems are transformed into smoothing equations with smoothing parameters by two-stage smoothing function,and then combined with the new nonmonotone line search technique,a nonmonotone smoothing Newton algorithm is constructed to solve the equations.Finally,a numerical example is given to illustrate the effectiveness of the proposed algorithm.