Study On Robust Solutions And Properties Of Multiobjective Optimization Problems

Study on robust solutions and properties of multi-objective optimization problems is an important research aspect in the field of the theory and methods of multi-objective optimization problems.This paper mainly focuses on some robust solutions and their properties of multi-objective optimization problems by means of Clarke directional deriva-tives,Clarke subdifferentials and linearized cones,including based on the two regular conditions defined by Burachik,two new robust regular conditions are proposed for the smooth,uncertain multi-objective optimization problems with inequality constraints,and then,the weak Kuhn-Tucker necessary condition for the robust efficient solutions and the strong Kuhn-Tucker necessary condition for the Geoffrion properly robust efficient solutions of the robust multi-objective optimization problems are established by using the robust regular condition;By means of linearizing cone in the sense of Clarke direction derivative,a kind of robust efficient solutions of the nonsmooth multiobjective optimization problems with inequality constraints is discussed and some optimality sufficient conditions for the problem are established.Chapter 1 mainly gives some research background and advancements of multi-objective optimization problems and some basic concepts.Chapter 2 mainly focuses on smooth,uncertain multi-objective optimization problems with inequality constraints.Firstly,based on the two regular conditions defined by Burachik,two new robust regularity conditions are proposed,namely Robust Guignard regular conditions and Robust Generalized Abadie regular conditions.Then,under the condition of Robust Guignard regularity,the weak Kuhn-Tucker necessary condition is established.Under the regular condition of Robust Generalized Abadie,we prove that Geoffrion properly robust efficient solutions guarantee Kuhn-Tucker properly robust efficiency,and under this condition,,stroing Kuhn-Tucker necessary conditions are established.Chapter 3 by means of linearizing cone in the sense of Clarke direction derivative,some optimality sufficient conditions are given for a kind of robust efficient solutions of nonsmooth multiobjective optimization problems with inequality constraints.Moreover,some concrete examples are also presented to illustrate the main results.The main results improve and generalize some recent research works.