Nonconvex Scalarization In Set Optimization With Set-valued Maps And Applications To Traffic Network

With the development of research on the theory of optimization with set-valuedmapping. Many research studies on this class of problems have used the criteria of setoptimization. In this paper, a set optimization problem is studied using a nonconvexscalarization function.The research in this thesis contains two parts. We study a nonconvex scalarizationfunction and how to use the nonconvex scalarization function to obtain some optimalityconditions for the set optimization problem in the first part. Then, we do some researchon the application of the function in the transportation network optimization.In the first part, a nonconvex scalarization function is introduced, some propertiesof the function are discussed. By virtue of the nonconvex scalarization function, someoptimality conditions for the set optimization problem are obtained without anyconvexity assumption.In the second part, we introduce another nonconvex scalarization function, and alsodiscuss some properties of the function. By virtue of the nonconvex scalarizationfunction, some optimality conditions for the set optimization problem are obtained. Asan application, a necessary and sufficient condition between a generalized weak vectorequilibrium flow and a generalized weak-equilibrium flow is established.