The Decompositional Augmented Lagrangian Function Method In Nonlinear Programming And The Decomposition Theory In The Vector-Valued Optimization

Nonlinear programming problems abound in many important fields such as engineering, national defense, finance etc. There are many ways to solve the problem of nonlinear planning in the small-scale problems. In order to solve the problem, the scale of the method is not much and the decomposition method is to solve the problem of a more efficient methods. In real life, decomposition methods can apply to many fields, e.g. Multi-regional power system analysis,Network design Price-and-resource directive schemes, and so on. Early in the sixties, some decomposition methods were proposed, such as Dantzig-Wolfe decomposition and Bender decomposition. Later in the eighties and nineties, a number of relevant research results about that came out. The aim of decomposition in optimization is to substitute large-scale optimization problems that present a structure of interrelated subsystems by solutions of sub-problems. In this thesis, one of research is the comparison of two decomposition approaches with the augmented Lagrangian function.Multi-objective optimization is forty years of rapid development of a new subject. As the most optimized an important branch, its chief research in a sense, a number of the question of the most optimized. Into eight, in the 1990s, the computer technology has developed rapidly. Optimization algorithms as springing up and the multi-objective optimization algorithms had made great strides in development. In this thesis, the other research is the vector-valued optimization decomposition theory for multi-disciplinary design optimization problems with mixed integer quasi-separable sub-systems.The present thesis is organized as follows. In Chapter 1, we firstly give a brief introduction to the development process of decomposition methods and some of the main decomposition methods, Secondly, we aim to introduce some of the main methods of multi-objective optimization;In Chapter 2, in order to overcome the classical Lagrangian relaxation (CLR) method and the augmented Lagrangian relaxation (ALR) method to solve the problem in optimization with faults, this chapter introduces the most widely used method—auxiliary problem principle (APP) method and block coordinate descent (BCD) method and we apply (APP) method or (BCD) method to the augmented Lagrangian relaxation method is to compare with the general solution of linear constraints z = Axof the question of applicability,finally numerically be duplicated theoretically example of the conclusions; In Chapter 3,we solve quasi-separable vector-valued optimization with decomposition methods in large scale systems and extends the necessary conditions for local weak Pareto solution and the necessary and sufficient conditions for global Pareto solution, and finally gave out value for example; In Chapter 4, we conclude the thesis and look forward to the future .