The Objective Penalty Function Method For Constrained Optimization Problems And Its Accuracy Research

With the development of information technology,optimization theory and methods is widely used in economic,science and technology,military and other fields,and has already became an independent discipline.Constrained nonlinear optimization problem and constrained minimax optimization problem is the most widely used.For solving constrained nonlinear optimization problem,the penalty function method is one of the most important tools.The penalty function method can transform a constrained nonlinear programming problem into an unconstrained nonlinear programming problem,and then gets the optimal solution of the constrained nonlinear optimization solution by solving the unconstrained penalty problem.For the traditional l₁ penalty function,the penalty parameter need to increase sequentially.But it is not efficient when the penalty parameter is too big in practical computing of Matlab.Therefore,the objective penalty parameter has been developed.In this paper,the main job is to propose two new classes of objective penalty functions for solving constrained nonlinear optimization problem and constrained minimax optimization problem.Based on the two new classes of objective penalty functions,the author develops two algorithms and proves the convergence of them separately.The structure of this paper is organized as follows:In Chapter 1,the author introduces the basic concept of the constrained nonlinear optimization problems,the constrained minimax optimization problem and then the objective penalty functions.What's more,the main job of the paper is introduced.In Chapter 2,for constrained nonlinear optimization problems,the author proposes a new class of objective penalty functions and lists several kinds of penalty functions which satisfying the conditions.Based on the new class of objective penalty functions,the author gets two theorems which establishes the relationship between the optimal solution of the original problem and the optimal solution of the unconstrained objective penalty problems.What's more,an algorithm is developed and the convergence of the algorithm is proved.Then the author lists five different objective penalty functions and compares the results of the given numerical examples for different objective penalty functions,which show that the proposed algorithm is efficient.In Chapter 3,for constrained minimax optimization problems,the author studies another new class of objective penalty functions and lists several kinds of penalty functions which satisfying the conditions.Based on the new class of objective penalty functions,the author proposes a new class of objective penalty functions with two parameters.Then the author develops an algorithm and proves the convergence of it.What's more,the author lists some different objective penalty functions and compares the results of the given numerical examples,which show that the proposed algorithm is efficient.In Chapter 4,the author summarizes the research contents of this paper,and proposes the directions for further research.