Research Of Quasi-Approximate Solutions For Multi-Objective Optimization Problem

Multi-objective optimization problems have been widely used in many fields,such as economy,finance,portfolio,algorithm design and so on,and have attracted the attention of scholars.The optimality condition is one of the important contents of the research on multi-objective optimization theory and its application.Considering that most of the solutions of many problems are approximate solutions,It is of great significance to study the optimality conditions of the approximate solution of the multi-objective optimization problem.This paper discusses the relationship between the quasi-approximate optimal solution of the optimization problem and the quasi-approximate(weak,proper)efficient solution of the multi-objective optimization problem through a new nonlinear scalar method for solving the general multi-objective optimization problem given in document;In fact,the necessary and sufficient conditions for testing the quasi-approximate(weak,proper)efficient solutions of multiobjective optimization problems are also obtained;It is worth noting that the results provided in this paper are obtained without any convexity and boundedness.In addition,this paper also analyzes a kind of model with piecewise linear structure of multiobjective optimization problem and has conducted an example analysis of it.