Operations research: mathematical aspects and applications.

Summary The 4th cover page states: "Optimization problems with combinatorial aspects, due to the presence of integer decision variables, are used in all sectors of economic life (investment, management of human resources or equipment, energy production planning) but also in technology (design of integrated circuits, optimization of telecommunication networks or on-line services). This book introduces the main principles of solving such problems, based on the theory of convex functions, duality in optimization, polyhedra and linear programming, methods of flow, dynamic programming, separation and evaluation, or integrity cuts. This overview includes two more advanced chapters, on applications in combinatorics of optimization under matrix positivity constraints (SDP optimization), and on interior point algorithms for convex quadratic programming. While relying on a rigorous mathematical analysis, this book presents numerous examples. In particular, a chapter of answers to a selection of exercises, as well as thirty or so problem statements with corrections, extend the course and provide illustrations from various fields of application.