Well-posedness For Parametric Weak Vector Equilibrium Problems

The concept of well-posedness is closely related to stability, approximation and numerical analysis. In recent years, with the development of the theory of vector optimization problem, the concept of well-posedness for scalar optimization problem was extended to vector optimization problem. And different concepts of well-posedness for vector equilibrium have been studied. This paper focuses on the concept of parametric weak vector equilibrium problems and its relation ship.The first chapter of this paper describes the research background of and study motivation.In chapter2of this paper introduces M-well-posedness and B-well-posedness for parametric weak vector equilibrium problems, Study the relationship between the two posedness, Gives the sufficient conditions for M-well-posedness and B-well-posedness by add some conditions to parametric weak vector equilibrium problems.In chapter3of this paper,on the basis of the concept of parametric well-posedness for parametric weak vector equilibrium problems, we Introduction the concept of strong parametric well-posedness for parametric weak vector equilibrium problems.And study it’s necessary and sufficient conditions. Then we compare the relationship between parametric well-posedness M-well-posedness and B-well-posedness.In chapter4of this paper, I make a brief summary and outlook.