Exact Penalty Function Of Objective Parameter

Nonlinear programming has an extremely wide range of applications inmanagement,engineering,science,and military aspects. Through long-standing researchand development of nonlinear programming problems, the current classical methodssolving such problems include feasible point method,Lagrange multiplier method,conjugate gradient method,penalty function method,trust region method and othermethods.These five methods prevalent following drawbacks:slow convergence,largeamount of computation and weak parameter sensitivity.The article discusses and fixesan exact penalty function method to solve the shortcomings of the previous algorithm.Penalty function method(including internal and external penalty function method)is an important method for solving constrained nonlinear programming problems. It isthe principle of transforming the constrained optimization problems into unconstrainedoptimization problems to make the process solving simple and efficient.Its solutionprocess is relatively simple and can effectively gets the optimal solution,so there are stilla lot of scholars in the study of the penalty function method in the world.In this paper,through combing the context of linear constrained optimizationproblem,nonlinear constrained optimization problems,imprecise penalty function andexact penalty function method related to the development of history,we focus on anexact penalty function of objective parameter.On the results of past scholars,we try toconstruct an exact penalty function of objective parameter and prove theorems. Throughdiscussing the nature of the exact penalty function,it shows that the method iseffective.Based on the theoretical proof,the paper gives the algorithm for solvingconstrained optimization problems.Numerical experiments show this method is effective.Compared with thetraditional penalty function method,this method is better in convergence and numericalresults.The main result of this paper:we creatively construct an exact penalty function andalgorithms associated with the objective function and constraint function.We discuss theexact penalty theorems of sufficient conditions and necessary conditions.In final,westudy the perturbation of relevant problems and illustrate the stability of the algorithm.