DC programming and DCA for solving some classes of problems in transportation and communication systemes
In this thesis, we focus on developing deterministic and heuristic approaches for solving some classes of optimization problems in Telecommunication and Mobility & Transport domain: Routing problems, Car pooloing problems, Power control problems in wireless network, Optimal spectrum balancing problems in DSL networks. They are large-scale nonconvex optimization problems. Our methodologies are focus on DC programming and DCA, Proximal decomposition method and Labeling method in graph theory. They are well-known as powerful tools in optimization. The considered problems were reformulated using the DC formulation/reformulation and exact penalty techniques and the DCA was used to obtain the solution. Also, depending on the structure of considered problems, we can provide appropriate DE decompositions or good initial points for DCA. All these proposed methods have been implemented with MATLAB, C/C++ to confirm the practical aspects and enhance our research works.