italian version

Aims :

To acquire the basic concepts on Optimization Theory and Operations Research.
To learn the methods and the strategies for modelling and solving linear and non-linear optimization problems.

Topics :

Problems, models and algorithms.
Unconstrained optimization: characterization of optimal solutions, iterative algorithms to find a local minimum. Convexity.
Constrained optimization: optimality conditions (KKT), Lagrange multipliers, sensitivity analysis.
Linear programming (LP): optimality conditions, geometric aspects of LP, simplex algorithm, degeneracy and cycling, artificial variables method.
LP Models: the diet problem, mixing problems, resources allocation problems, cutting problems, production planning problems, inventory management problems, transport problems, assignment problems.
Duality theory: dual problem, weak and strong duality theorems, relationships between the primal and the dual problem, Farkas lemma, economical interpretation of duality, sensitivity analysis.

Textbooks :

M. Fischetti, "Lezioni di Ricerca Operativa", Edizioni Libreria Progetto, Padova (1995).

C. Mannino, L. Palagi, M. Roma, "Complementi ed Esercizi di Ricerca Operativa", Ingegneria 2000, Roma (1998).

F. Pezzella, E. Faggioli: Ricerca Operativa. Problemi di Gestione della Produzione, Pitagora editrice.
J. Nocedal, S. J. Wright: Numerical Optimization, Springer Verlag.
V. Chvàtal: Linear Programming, Freeman & Co. New York.
Dispense del docente e altro materiale didattico (presentazioni Powerpoint, ecc.).

Exam :

A written test and an oral one. Only students having obtained a positive judgement on the written test can accede to the oral test.

Tutorial Session :

To be agreed with the students during the course.