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Basic Information

Course Unit Title: OPTIMIZATION METHODS

Course Unit Code: 540AA

Level of course unit

Second cycle degree programme in Embedded Computing Systems

Year of study

First year

Semester when the course is delivered

Second semester

Number of ECTS credits allocated: 6

Name of Lecturer(s):

Prof.: Mauro Passacantando
Email: mauro.passacantando@unipi.it

Language of instruction

English

General Information

Learning outcomes

The student who successfully completes the course will be able to demonstrate a solid knowledge of the methodologies and algorithms concerning solution of advanced nonlinear optimization problems and equilibrium problems. He/she will acquire ability in formulation of advanced mathematical models of decisional problems. The student will also be aware of the advanced theory of nonlinear optimization and equilibrium problems.

Course contents

Nonlinear optimization: existence and uniqueness of optimal soluitons, optimality conditions, duality, gradient methods, Newton and quasi-Newton methods, penalization methods.
Multiobjective optimization: partial order, Pareto optimal solutions, optimality conditions, scalarization approach. Solution methods: no-preference methods, a-posteriori methods, a-priori methods.
Non-cooperative game theory: Nash equilibrium, matrix games, pure and mixed strategies, existence of equilibria, bimatrix games, games with infinite strategies: relationships with variational inequalities.

Specific Information

Prerequisites, co-requisites, as a prerequisite for further study

Prerequisites

None.

Co-requisites

None.

Prerequisite for

None.

Mode of delivery

Delivery

face to face

Attendance

Advised

Teaching methods

• Lectures

Learning activities

• Attending lectures
• Individual study

Recommended or required reading

Lecture notes are available online. Recommended reading includes the following works:

[1] S. Boyd and L. Vandenberghe, Convex optimization, Cambridge University Press, 2004.

[2] M.S. Bazaraa, H.D. Sherali, C.M. Shetty, Nonlinear Programming: Theory and Algorithms, Wiley-Interscience, 2006.

[3] J. Gonzalez-Dia, I. Garcia-Jurado and M.G. Fiestras-Janeiro, An introductory course on mathematical game theory, A.M.S. Vol.115, 2010.

[4] R. Fourer, D.M. Gay, B.W. Kernighan, Ampl: A Modeling Language for Mathematical Programming, Duxbury, 2002.

Assessment methods and criteria

Assessment methods

• Final oral exam
• Final written exam

Assessment criteria

During the written exam (3 hours) the student is asked to solve exercises in order to demonstrate the ability to put into practice the basic algorithms of advanced optimization and equilibrium models.

Work placement

No