Characterizations Of The Solution Set For Robust Convex Multiobjective Optimization Problems

Because the real world multiobjective optimization often have measurement or predic-tion errors,it extends an important research field in the theory and method of multiobjective optimization,that is,robust multi-objective optimization problems.This paper mainly discusses the multiobjective robust convex optimization problem for a class of uncertain data.Firstly,a robust counterpart under general uncertain sets is given,and then the robust multiobjective counterpart is transformed into a robust single objective convex optimization problem by using the scalar method.Then we obtain robust solution of scalar multiplier characterization,and for the scalar robust convex optimization problem by constant differential property and constant Lagrange property of general in the robust so-lution set.Finally the robust characterization of robust convex multiobjective optimization problems of the proper efficient solution set are obtained by previous properties.Chapter 1,the research background,solution properties and research status of mul-tiobjective optimization problems and robust multiobjective optimization problems are given,and some fixed marks and definitions needed in this paper are given.Chapter 2,the problem of robust convex multiobjective optimization is transformed into a single-objective robust convex optimization problem by scaling method.By using multi-objective knowledge,it is proved that the discouragement of the scaling robust single-objective optimization problem is the Geoffrion effective solution of the robust convex multiobjective optimization problem,and the necessary and sufficient conditions for the scaling robust solution are obtained by normal cone and Lagrange duality.Chapter 3 mainly studies the characterization of the subset of true efficient solutions for robust convex multiobjective optimization problems.Firstly,from the convexity and compactness of uncertain sets,the constant Lagrange properties and theorems for robust single objective optimization problems are obtained.Through these properties and the concept of subdifferential,we obtain the characterization and related theorems of the subset of proper effective solutions for robust convex multiobjective optimization problems with a given robust solution point.