An Exact Penalty Function Method For Nonlinear Programming Problems That May Not Be Feasible

This paper deals with the problem of nonlinear programming.At present,the solving of a lot of constrained optimization problems are established in the non empty feasible domain under the premise,but in the actual application process,the feasible domain of optimization problem may be empty.At this time,if you still use the previous algorithm,you may waste a large amount of calculation time and couldn't find the optimal solution.If the algorithm can find out whether the problem is feasible as soon as possible,it can save time.Therefore,in this paper,the exact penalty function method is discussed and its global convergence is analyzed under the assumption that the problem may not be feasible.We prove that in finite iterations,the algorithm can detect that the problem is not feasible,or find an approximate feasible/optimal solution with arbitrary accuracy.Through numerical experiments,it is proved that the algorithm is reliable for the different exact penalty functions whitch is proposed in the literature.The main contents of this article are as follows:The first chapter is the introduction part.First,we introduce the research background and present situation of possible infeasible problems.Secondly,we introduce the significance and main research content of this paper.In the second chapter,we focus on the nonlinear equality constrained opti-mization problem.Based on the penalty function whitch is proposed in this paper[24],we propose an unfeasibility test for equality constrained optimization problem.we can detect the infeasibility of the problem as soon as,and make the algorithm stop.This way to solve the possible infeasible problems use the switch to decide whether the current iteration should seek the optimal solution of nonlinear programming or determine that the planning problem is not feasible.In this part,we will prove the effective-ness of the infeasible detection in the exact penalty function method and give its algorithm implementation.The third chapter,we focus on the nonlinear inequality constrained optimiza-tion problems.For the problem of inequality constrained optimization,we propose a corresponding exact penalty function algorithm.Similar to the second chapter,we also propose unfeasibility detection so that the algorithm can quickly determine whether the problem is feasible.If the problem is not feasible,the algorithm stops,if the problem is feasible,the algorithm will continue to run,and can quickly find the optimal solution of the problem.In this part,we use the famous Kissing Number problem to prove the effectiveness of the infeasible detection in the exact penalty function method and give its algorithm implementation.