Research On Methods For Nonsmooth Optimization And Multiobjective Programming

The paper aims to obtained a new method for a special nondifferentiable problem, Piecewise smooth optimization,and applys it to multiobjective programming to get a new minmax method.For the purpose, the research on the methods and the classifications of nonsmooth optimization,with their advantages and disadvantages commented, is needed.On the basis, a new idea on solving nondifferenti-able problems is brought forward and then the new method is presented. After the research on the methods for multiobjective programming, A new minmax method for multiobjective programming is produced by the applying of the new method .At the end,an important numerical experience is made to show the achievement of the new method.The paper is divided into five chapter, as follows:In the first chapter,the history of the both problems above is revealed and the relationship between them is pointed out.The second chapter mainly presents the basic concepts and theories,which are related to convex analysis, nonsmooth differentiable theory and kinds of solutions of multiobjective programming.The third chapter is devoted to the crucial part of the paper. Two classes of basic methods for non-smooth optimization,Subgradient method and Bundle method, are researchedDuring the course,the advantages and disadvantages are commented on, which brings us a new idea to solve the piecewise smooth problem.Subsequently a new algorithm is obtained with several ways to implement Moreover, the convergence of the new method is shown and the relationship between the Two classes of basic methods and the new method is referred to.The methods for multiobjective programming are considered in chapter four. According to the participations of the decision-maker, the methods are divided into four group,no preference methods, posteriori methods,priori methods,interactive methods.With the help of the new method in chapter third,one can get a new minmax algorithm.The last chapter concentrates on the numerical experience.With the results,the paper compares the new algorithm with several classical algorithms on the convergence rate.On the other hand, With figures and another numerical results,the paper tests the convergence and the stability of the new method..