Book “Lezioni di Ricerca Operativa” (in Italian): .  M. Fischetti, ” Worst-Case Analysis of an Approximation Scheme for the Subset-Sum Problem”, . Teacher in charge, MATTEO FISCHETTI · [email protected], MAT/09 Matteo Fischetti, Lezioni di Ricerca Operativa. Padova: Progetto, Cerca nel . Main course: Ricerca operativa e Ottimizzazione / Operation Research And Optimization Matteo Fischetti, Lezioni di Ricerca Operativa. Progetto Libreria.
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Learn algorithmic techniques for some combinatorial optimization problems. Being able to formulate and solve combinatorial optimization problems using integer linear programming.
Understand the complexity of the problems studied. Acquire ifschetti knowledge of Optimization problems and of the mathematical modeling techniques for complex decisions.
Acquire the knowledge of some solution algorithms for Linear Programming problems. Acquire the ability to recognize optimization problems and develop mathematical models of decision-making problems.
Acquire the ability of computing solutions of linear programming problems. Acquire autonomy in modeling and algorithmic choices for problems related to complex decision-making. Be able ricrrca hold a conversation and to read texts on topics related to the modeling of decision problems and Linear Programming. Acquire the ability of upgrading flexible knowledge and skills in the field of Optimization and related problems that arise in various areas, such as mathematics, computer science and management science.
DISIM Teaching Website – University of L’Aquila :: Course Detail
The course profile, written following the Tuning international methodology foschetti, is available here. Bachelor Degree in Computer Science: Claudio Arbib Stefano Smriglio. Elements of computational complexity: Transversal vertex-coverstable set, dominating set, edge-cover, perfect matching, knapsack, graph colouring chromatic number and indexshortest path, spanning subgraph etc.
Formulation as linear programming. Unimodular and totally unimodular matrices.
Lezioni di ricerca operativa
Necessary conditions, sufficient conditions. Oezioni hull and ideal formulation of an integer LP. Fundamentals of duality theory in LP. Matroids and the Greedy Algorithm. Basics of linear algebra: Rank of a matroid. Support function of a convex set. Matroid polyhedron, matroid intersection, intersection of two submodular polyhedra]. Guaranteed approximation algorithms for CO. Linear relaxation of a mixed integer linear program. Dichotomy on a fractional variable. Tips on the Ellipsoid Method.
Solution of LP with exponentially many variables, example: Module Ricerca Operativa Optimization problems: Learning Outcomes Dublin Gischetti On successful completion of this course, opeerativa student should Module Ottimizzazione Combinatoria Being able to evaluate the general complexity of combinatorial optimization problems.
Being able to formulate si as linear programming. Know basic primal-dual relations. Know elementary matroid theory, dynamic programming. Have the notion and know the main properties of unimodular matrices. Have basic notions on algorithm and problem complexity. Know standard algorithms for spanning tree, bipartite matching, shortest path. Know heuristics for the TSP and Knapsack. Evaluate the complexity of an algorithm and, for simple cases, of a problem.
Be able to recognize whether a matrix is, or is not, totally unimodular. Solve by standard algorithms the spanning tree, bipartite matching, knapsack, optimal path, travelling salesman problem. Lezoini combinatorial optimization problems, or binary optimization problems derived from applications, as linear programming.
Understand when a problem has the shape of a matroid and what is the advantage. Know what is the advantage of a totally unimodular matrix.
Decide when it is convenient to use dynamic programming. Realize the limits of heuristics. Prove rigorously a simple theorem. Prove or disprove by counterexample a simple conjecture. Understand the role played by combinatorial optimization in applications.
Address submodular set functions, polyhedral combinatorics, advanced integer linear programming. Acquire the ability of computing solutions of linear programming problems Acquire autonomy in modeling and algorithmic choices for problems related to complex decision-making Be able to hold a conversation and to read texts on topics related to the modeling of decision problems and Linear Programming Acquire the ability of upgrading flexible knowledge and skills in the field of Optimization and related problems that arise in various areas, such as mathematics, computer science and management science.
Textbooks Module Ottimizzazione Combinatoria W.
Dover Books on Computer Science. Sassano, Modelli e Algoritmi della Ricerca Operativa. Tsitsiklis, Introduction to Linear Optimization. Matteo Fischetti, Lezioni di Ricerca Operativa. Opegativa Teaching Resources Homepage: Click here to access the teaching material available on this site last update: Teaching material available on the external website http: Recent teaching material This list contains only the latest published resources. Fiischetti marked with an asterisk belong to other courses indicated between brackets.
Course page updates This course page is available with possible updates also for the following academic years: