Necessary conditions for the optimality of a second order sweeping process

In this thesis, the necessary conditions for the optimality of a second-order sweeping process are studied. This thesis consist of five chapters. The first chapter, the introduction, is about the history of optimality and the sweeping processes. In the second chapter, necessary information and definitions for the thesis are given. The second chapter consists of five sections. In this chapter, first of all, informations about subjects such as convex sets, convex functions and convex multivalued mappings are given, and then sweeping processes are expressed. In the last part, information about convex programming problems are given. In the third chapter, the tools and methods used throughout the thesis are mentioned. The fourth chapter, the results section, constitutes the main part of our thesis. In this section, the valid constraints applied to the trajectory and its derivative and the necessary conditions for the optimality of a second-order sweeping process are discussed and formulated. In the fifth chapter, the general evaluation of our thesis study has been made and suggestions about the subject have been given.