This course aims to introduce the student to some basic models and to the main methodologies in the optimization field, with a particular attention to dynamic programming, combinatorial optimization, graphs, linear programming. Complexity theory is introduced and used as a tool and the role of integer linear programming within the OR community is illustrated.
Basic notions: models and algorithms, computational complexity, recursion and induction, invariants and monovariants, graphs, convex sets, polyhedra and cones.
Some of the models in Dynamic Programming: maximum increasing subsequence, maximum common subsequence, knapsack models.
Some of the models in graphs: Eulerian ed Hamiltonian paths and cycles, planar graphs and their duals, bipartite graphs, shortest paths, minimum spanning trees, max flow/min cut, maximum matching.
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.
A more detailed program as intended, the day-by-day program of the last edition of the course, and the ongoing program of the current edition are available at the web-page of the course:
Written final examination.
Past exams with answers can be found at the web-page of the course:
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