This course aims to introduce the student to some basic problems in the optimization field, with a particular attention towards the linear programming and some network optimization problems. Besides, basic notions of integer and combinatorial programming will be outlined. The course also includes some hours dedicated to practical exercises, with the aim of addressing the student to the mathematical formulation of a problem and its subsequent solution.
Basic notions: convex sets, polyhedra and cones; convex functions and convex programming.
Linear programming: mathematical formulation of linear programming problems; equivalent forms, standard form; mathematical structure, geometry of linear programming, properties.
The simplex algorithm: vertices and basic solutions; optimality conditions; tableau method, auxiliary problem, two-phases method.
Duality theory: the fundamental duality theorem of linear programming, the dual simplex algorithm; economic interpretation; sensitivity analysis.
Integer linear programming: the cutting plane method; the branch and bound.
Network optimization: the minimum spanning tree problem, the shortest path problem, the maximum flow problem.
|FISCHETTI M.||Lezioni di Ricerca Operativa||Edizioni Libreria Progetto Padova||1999||8887331049|
Written final examination.