Complements of Operating Research
A.Y. 2019/2020
Learning objectives
The course aims to broaden the foundations of mathematical programming. The problems of nonlinear optimization will be addressed and the techniques to face linear and integer linear programming problems will be deepened.
Expected learning outcomes
Ability to choose the most suitable tools to solve non-linear optimization problems. Ability to apply decomposition techniques to deal with integer linear programming problems, skills related to the techniques used by commercial solvers.
Lesson period: First semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
Course syllabus and organization
Single session
Responsible
Lesson period
First semester
Course syllabus
Non Linear Programming. Unconstrained optimization: analytical optimality conditions, conditions for the convergence of iterative methods. Quasi-Newton and Trust-Region methods. Constrained optimization: analytical optimality conditions (KKT). Algorithms: outline of penalty and barrier methods, augmented Lagrangians and SQP.
Integer Linear Programming. Model preprocessing techniques. Lagrangian relaxation and subgradient technique. Column generation method and Pricing techniques for specific problems (Cutting Stock, Location). Polyhedral techniques. Model reinforcement. Separation and cutting plane techniques for specific problems (TSP, Knapsack).
Laboratory: modeling languages (Ampl or similar). Description of solvers (Cplex, Gurobi, Snopt).
Integer Linear Programming. Model preprocessing techniques. Lagrangian relaxation and subgradient technique. Column generation method and Pricing techniques for specific problems (Cutting Stock, Location). Polyhedral techniques. Model reinforcement. Separation and cutting plane techniques for specific problems (TSP, Knapsack).
Laboratory: modeling languages (Ampl or similar). Description of solvers (Cplex, Gurobi, Snopt).
Prerequisites for admission
The student should already have the skills acquired in an Operations Research course.
In particular, it is required to know the Linear Programming and the Integer Linear Programming foundations, the primal / dual properties and those of orthogonality (or complementary slackness).
In particular, it is required to know the Linear Programming and the Integer Linear Programming foundations, the primal / dual properties and those of orthogonality (or complementary slackness).
Teaching methods
Lectures and computer lab hours.
Teaching Resources
Lecture notes on Non Linear Programming.
Excerpts from L. Wolsey. Inger Programming. Wiley-Interscience, 1998.
Excerpts from D.S: Chen et al. Applied Integer Programming. Modeling and Solution. Wiley, 2010.
Excerpts from L. Wolsey. Inger Programming. Wiley-Interscience, 1998.
Excerpts from D.S: Chen et al. Applied Integer Programming. Modeling and Solution. Wiley, 2010.
Assessment methods and Criteria
The exam consists of an interview and one of the following two options:
- the individual development of a project for the solution of a ILP model,
- the deepening of a research article (agreed with the teacher) on one of the main techniques addressed in the course.
The types of models proposed for the projects require the use of one of the techniques described in the course.
The tools (modellers and solvers) necessary to carry out the project can be both those seen in the laboratory, and others chosen by the student and agreed with the teacher.
The interview is aimed at verifying the competences related to the theoretical aspects treated in the course, and to discuss the chosen project.
- the individual development of a project for the solution of a ILP model,
- the deepening of a research article (agreed with the teacher) on one of the main techniques addressed in the course.
The types of models proposed for the projects require the use of one of the techniques described in the course.
The tools (modellers and solvers) necessary to carry out the project can be both those seen in the laboratory, and others chosen by the student and agreed with the teacher.
The interview is aimed at verifying the competences related to the theoretical aspects treated in the course, and to discuss the chosen project.
MAT/09 - OPERATIONS RESEARCH - University credits: 6
Lessons: 48 hours
Professor:
Trubian Marco
Shifts:
-
Professor:
Trubian MarcoProfessor(s)