The Research And Application Of The Well-Posedness Of A Class Of Non-Convex Optimization Problem Solvings

The data of problem is often disturbed in real life,we often calculate solution of the perturbed problem to approximate the solution of the original problem.Therefore,the stability of the solution set of the original problem is an important issue.In this paper,we consider a class of non-convex vector optimization problems with two mapping differences.By taking advantage of appropriate convergence and convexity of the two mappings,the stability results of the nonconvex vector optimization problem is obtained,when the data of approximate problem converges to the data of original problem data in the sense of Painlevé-Kuratowski convergence.Well-posedness is also an important part of stability research,the second part of this paper considers the population game problem,because the payment function of this problem is not limited by convexity conditions,so the qualification of such non-convex mathematical economic models is studied.Firstly,under the condition that the population state function is pseudo-continuous,the existence theorem of cooperative equilibrium for the population game problem is established.Secondly,the Hadamard and Levitin-Polyak well-posedness of cooperative equilibrium for population game problems are introduced,and the adequacy conditions for the establishment of these two well-posedness concepts are established.