Several Classes Of Filled Penalty Functions And Their Algorithms For Solving Global Optimization Problems

An important method to solve constrained optimization problem is to approach the optimal solution of constrained optimization problem gradually by sequential uncon-strained optimization method,namely penalty function method.And the filling function method is one of the effective methods to solve the global optimal problem.In this paper,several classes of objective penalty functions and penalty functions with filling properties are proposed to solve non-convex constraint optimization problems,and the theoretical properties of these functions,such as exactness,smoothness,global convergence,are dis-cussed.On this basis,the paper gives out local optimization algorithm,global optimization approximate algorithm and corresponding examples are given for solving constrained op-timization problems.This paper consists of six chaptersThe first chapter briefly introduces the basic knowledge of optimization theory used in this paper,presents the basic concept of penalty function and filling function for solving optimization problemsIn Chapter 2,two classes of objective penalty functions,the penalty part of the new penalty functions smoothly approximate to the penalty part of l1 exact penalty function,are proposed for constrained optimization problems.The exactness of these two penalty functions is proved respectively,that is,the optimal point of penalty function coincides with that of original optimization problem.At the same time,two local optimization algorithms based on the two classes of objective penalty functions are proposed in this chapter.And it is proved that the cluster points of the iterative point sequence obtained by the algorithm are both feasible solutions and locally optimal solutions of the original optimization problem.Numerical experiments are also given to illustrate the practicability of the two local optimization algorithmsThere are two main difficulties to solve the global optimization problem:one is how to find a better locally optimal solution from the current one;the second is how to judge that the current point is global.The filled function method is one of the best methods to solve the first difficulty.In Chapter 3,a class of exact lower-order penalty functions with filling properties is proposed and a local optimization algorithm is given and the cluster points of the iterative point sequence in this algorithm satisfy the KKT condition of the original problem.On the basis of this current KKT point,we constructed a filled lower-order objective penalty function,and the exactness and global convergence are maintained Then,the global optimization algorithm based on the filled penalty function was given and the termination point was proved to be the globally approximate optimal solution of the original optimization problem.The numerical experimentresults in this chapter also show that the two algorithms have practical applicationIn Chapter 4,a class of exact augmented Lagrangian objective penalty function is proposed.Based on this function,a local optimization algorithm is given the convergence of the sequence of iterative points obtained by this algorithm is proved.Then,a class of augmented Lagrange objective penalty functions with filling properties is given,the purpose of which is to use the penalty functions with filling property to find a locally optimal solution that is better than the current one.On the basis of the exactness and filling properties of this function,the algorithm for solving the global optimization problem is given in this chapter.It is proved that the terminating point of the algorithm is the globally approximate optimal solution of the optimization problem and the numerical calculation is carried outIn Chapter 5,a class of piecewise objective penalty functions is proposed,and the exactness of this penalty function is proved.A local optimization algorithm based on this penalty function is given.A new class of piecewise objective penalty functions with filling properties is proposed in this chapter.The exactness and filling properties of this penalty function are both proved,and an algorithm for finding the globally optimal solution is designed and the numerical results are givenChapter 6 summarizes the main work of this thesis,the influence of different algo-rithms on constrained optimization problem is analyzed and makes a further plan for the future research.