Non-monotone Smoothing Algorithm For Equality And Inequality System With Penalty Factor

Equality and inequality are widely used in data analysis,set separation,computer-aided design and other fields,and how to effectively solve the problem of equality and inequality system is of great significance.In this paper,based on the original smooth algorithm for solving equality inequality system,penalty factor is added to the smooth algorithm from the function characteristics,so as to make the algorithm for solving equality inequality system more efficient.(1)The nonlinear inequality system is transformed into non smooth equations by means of projection,and then the system is transformed into smooth equations with smooth factor by using the idea of smooth reconstruction and a special piecewise smooth function.The decreasing speed of smooth factor is controlled by increasing the penalty factor,so as to meet the requirements of numerical calculation,Finally,a smooth Newton algorithm with penalty factor is given,and the global convergence and local superlinear(or local quadratic)convergence of the algorithm are proved.The numerical results show that the algorithm is feasible.(2)In this paper,the smooth Newton method with penalty factor is applied to solve equations and inequalities,which expands the application scope of the algorithm and makes it more general.At the same time,the non monotone linear search technique is introduced to increase the computational efficiency of the algorithm.Numerical experiments are carried out on some typical examples by using the non monotone smooth algorithm with penalty factor in MATLAB,The results show that the improved algorithm speeds up the iteration speed.It also proves that the algorithm is suitable for solving the inequality problems with unequal number of variables and inequalities.The numerical experiment results show the effectiveness of the algorithm.