Levitin-polyak Well-posedness Of Vector Equilibrium Problems

Vector equilibrium problem is an important concept of the system under development, we now know a lot of problems can be reduced to balance the issues, such as:Optimization problems, Nash equilibrium problems, Complementarity problems, Fixed point problems, Saddle point theorem and so on. Therefore, the balance of the study also contributed to the development of these disciplines.It is well known that the well-posedness is very important for both optimization theory and numerical methods of optimization problems, which guarantees that, for approximating solution sequences, there is a subsequence which converges to a solution. So, it is of importance not only in theory but also in practical applications. This paper studies the generalized LP well-posedness of vector equilibrium problems and LP well-posedness of vector quasi-equilibrium problems, and draw some relevant conclusions.In chapter 1, an overview of the LP well-posedness of vector equilibrium problems of the balance of academic significance and relevance vector balance of qualitative research profile.In chapter 2, first introduced the LP well-posedness of vector equilibrium problems of the balance of some basic concepts and some of its prescriptive instructions. Second, consider the adoption of the Kuratowski measure of non-compactness of vector equilibrium problems come under the categories of LP well-posedness theorem. Once again we introduce gap function given an optimization problem model, and concludes that the balance of the LP well-posedness of optimization problems and the relevance of qualitative relations. Finally the introduction of real-valued function of real-valued function obtained with the vector of the appropriate balance between qualitative relationship. And gives a number of related criteria and characterizations.In chapter 3 of this article looks like the second chapter, on this basis, the LP well-posedness of the research extended to the vector quasi-equilibrium problems, and draw the relevant conclusions.