ECTS - University of Pisa
Scheda programma d'esame
OPTIMIZATION METHODS
MAURO PASSACANTANDO
Academic year2016/17
CourseEMBEDDED COMPUTING SYSTEMS
Code540AA
Credits6
PeriodSemester 2
LanguageEnglish

ModulesAreaTypeHoursTeacher(s)
OPTIMIZATION METHODSMAT/09LEZIONI60
MAURO PASSACANTANDO unimap
Programma non disponibile nella lingua selezionata
Learning outcomes
Knowledge

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.
Assessment criteria of knowledge

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.

Methods:

  • Final written and oral exams
Teaching methods

Delivery: face to face

Learning activities:

  • attending lectures
  • individual study

Attendance: Advised

Teaching methods:

  • Lectures
Syllabus

Nonlinear optimization: existence and uniqueness of optimal soluitons, optimality conditions, duality, gradient methods, Newton and quasi-Newton methods, penalization methods, barrier methods. Multiobjective optimization: partial order, Pareto optimal solutions, optimality conditions, scalarization approach, goal method. Non-cooperative game theory: Nash equilibrium, matrix games, pure and mixed strategies, existence of equilibria, bimatrix games, games with infinite strategies, gap and D-gap functions.
Bibliography

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

  • S. Boyd and L. Vandenberghe, Convex optimization, Cambridge University Press, 2004.
  • M.S. Bazaraa, H.D. Sherali, C.M. Shetty, Nonlinear Programming: Theory and Algorithms, Wiley-Interscience, 2006.
  • J. Nocedal, S. Wright, Numerical Optimization, Springer Series in Operations Research and Financial Engineering, 2006
  • A.R. Conn, K. Scheinberg, L.N. Vicente, Introduction to Derivative-Free Optimization, SIAM series on Optimization, 2009
  • D.T. Luc, Theory of Vector Optimization, Springer, 1989
  • Y. Sawaragi, H. Nakayama, T. Tanino, Theory of Multiobjective Optimization, Academic Press, 1985
  • M.J. Osborne, A. Rubinstein, A Course in Game Theory, MIT press, 1994
  • N. Nisan, T. Roughgarden, E. Tardos, V.V. Vazirani, Algorithmic Game Theory, Cambridge University Press, 2007 
Updated: 02/05/2017 12:44