| Since the 1940s,with the development of science and technology and the wide applica-tion of electronic computer,the optimization theory and algorithm quickly developed into an independent discipline.With the rapid development of computer technology,optimization theory and methods are widely used in public management,economic management,engi-neering construct,military,defense and other fields.The constrained nonlinear programming problem is a common problem.The solving process of constrained nonlinear programming is complicated,which can often be converted into unconstrained nonlinear programming problem.Penalty function method is one of the most commonly used methods.It gets the solution of the constrained programming problem by solving the unconstrained penalty problem.Exact penalty function is that when the penalty parameter is sufficiently large,the optimal solution of constrained programming problem is obtained by solving the optimal solution of unconstrained programming problem.The so-called simple penalty function is that the penalty function contains the constraint functions and the objective function of the original problem and does not contain their gradient information.For the traditional penalty function,if it is simple,it can not be both exact and smooth.The exact penalty function of the present study is mostly simple and not smooth,so the smoothing of the exact penalty function becomes particularly important.The objective penalty function method is to introduce penalty parameter for the objective function.This paper mainly consists of four chapters.In Chapter 1,the author mainly introduces the basic knowledge of constrained optimiza-tion problems and the penalty function method.In Chapter 2,a new smoothing method is proposed for the new exact objective penalty function with two parameters.It is proved that the optimal solution of the smooth objective penalty problem is the approximate optimal solution of the original problem.An algorithm is designed based on this objective penalty function.The algorithm can be shown to be convergent under some mild conditions.The feasibility of the algorithm is illustrated with some numerical examples.In Chapter 3,on the basis of the smooth function proposed in Chapter 2,the l1exact penalty function is approximated,the algorithm is designed and its feasibility is illustrated with some numerical examples.In Chapter 4,the smoothness of the new lower order exact object penalty function is studied,and a new smoothing method is presented based on the smooth objective penalty function.It is proved that the optimal solution of the smooth objective penalty problem is the approximate optimal solution of the original problem,and it is proved that the algorithm is convergent.In Chapter 5,the research content of this paper is summarized and the direction of future research is introduced. |
