A New Exact Penalty Function Method For Solving Semi-infinite Programming Problems

The semi-infinite programming problem is an optimization problem that solves an infinite number of constraints or an infinite number of decision variables.It is a very important research field in mathematical planning.In the anti-seismic system design,multi-terminal input and output control systems,wide-band amplifiers and robot trajectory planning and other aspects have a wide range of direct applications.Therefore,the study of theoretical knowledge and numerical algorithm experiments on semi-infinite programming problems has a strong application value and has attracted the attention and research of the majority of scholars at home and abroad.For semi-infinite programming problems,this paper provides a new generalized exact penalty function,which contains many commonly used penalty functions as special cases.It is proved that under the condition of proper constraint specification,when the penalty parameter is sufficiently large,the local optimal solution to the penalty problem is the local optimal solution to the original problem.In addition,under the appropriate conditions,this paper also proves that the global optimal solution sequence of the penalty problem converges to the global optimal solution of the original problem.Further,when the solution to the penalty problem is not an exact solution,another accurate penalty algorithm and its convergence analysis are given in this paper,and a globally approximate optimal solution to the original problem is obtained.The main content of this paper is organized as follows:The first chapter is the introduction part.This part briefly introduces the research background and status of the semi-infinite programming problem.Second,the research significance and main research contents of this paper are expounded.In the second chapter,a new class of exact penalty functions is proposed to solve the problem of semi-infinite programming.First,under the appropriate conditions,it is proved that the local optimal solution sequence of the related penalty problem is the local optimal solution of the original problem.Second,under the appropriate constraint specifications,when the penalty parameter is sufficiently large,it is proved that the global optimal solution to the penalty problem also converges to the global optimal solution to the original problem.It is worth mentioning that the exact penalty function in this paper is not a specific exact penalty function,but an exact penalty function that satisfies the generality under certain conditions.In the third chapter,under the exact penalty function provided,the exact penalty algorithm for solving semi-infinite programming problem and its numerical experiment are given.Considering that if the exact solution to the penalty problem is more complicated,another accurate penalty algorithm is given to solve the global approximate optimal solution of the penalty problem,and then a global approximate optimal solution to the original problem is obtained.