Study On Optimality Condition And Scalarization Of The Properly Efficient Solutions To Multi-objective Programming

The multi-objective programming is widely used in industrial production,material transportation,agricultural planting and other fields.The Optimality condition and scalarization are the core of multi-objective programming theory and application,especially,the study of properly efficient solutions in these two aspects has attracted much attention from the academic community.According to the attributes of the data in the model,the problem can be simply divided into mathematical programming and uncertain mathematical programming,and it's also worth pointing out that the robust optimization method is proved to be one of the effective methods to deal with uncertain multi-objective programming.This paper mainly uses the knowledge of convex analysis and non-smooth analysis to study the optimality conditions and scalarization of properly effective solutions for(uncertain)multi-objective programming problems,the main contents are summarized as follows:In the first part,the optimality conditions and duality theorems of properly efficient solutions for a class of uncertain multi-objective programming problems are studied by using robust optimization method.Firstly,the concept of robust true effective solutions is introduced,and the corresponding scalarization theorem are established.Secondly,we present the optimality conditions under the assumption of closed convex cone constraint qualifification.Finally,for the Wolfe type dual problem to the primal uncertain multi-objective optimization,the strong and weak duality theorems are proposed for properly efficiency.In the second part,the scalarization theorem of quasi properly effecient solution for a class of unconstrained multi-objective programming problems is studied.Firstly,under two improved Pascoletti-Serafini scalarization optimization models,the original multi-objective programming problems with quasi properly effecient solution and the scoring conditions of the approximate optimal solution of the corresponding scalarization optimization problem.Secondly,for a class of extended Pascoletti-Serafini scalarization problems,the relationship between the quasi properly effecient solution of the original multi-objective programming problem and the optimal solution of the scalarization problem is revealed.