Research On Smoothing Newton Methods For Two Optimization Problems

Optimized theory is a branch of applied mathematics,it is a discipline with wide application,while linear planning is a key branch of the optimized problem.Linear planning develops rapidly with wide application scope,it can assist in people's scientific management,explore the limit value of linear objective goal under linear limitation condition,and is widely applied in areas such as military combat,economic analysis and operative management.Smoothing Newton method is a common way to solve the issue of linear planning,in order to solve the issue of linear planning and its antithesis issue,generally speaking corresponding K-K-T system is established for discussion.But the constraint conditions in the system is normally very complex.In order to avoid the complexity,the paper is supported by the relatively complemented FB function to construct a new smooth approximate function,based on this smooth function,transfer K-K-T system into approximate smooth function equations to solve it.Corresponding smoothing Newton algorithm is set up making use of the property of smooth function,in addition to further analysis of the feasibility and convergence of the algorithm.Numerical experiment also testifies that the algorithm is effective.On the linear relatively complementary issue,Mangasarian considered to solve the absolute value function equation transferred from linear relatively complemented issue of equal value.On this basis,we construct a smooth approximate function of the function of absolute value,and set up a variety of smoothing Newton algorithm solving linear relatively complemented issue making use of this smooth approximate function,and further testifies the overall convergence and partial quadratic convergence.The numerical result has also fully proved that the algorithm is effective.Finally we have provided two other varieties of smoothing Newton algorithm based on relatively complemented function,and have compared the advantages and disadvantages of the two algorithms through numerical experiment.