Second cycle degree programme in Embedded Computing Systems
Prof.: Mauro Passacantando
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.
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.
face to face
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. Gonzalez-Dia, I. Garcia-Jurado and M.G. Fiestras-Janeiro, An introductory course on mathematical game theory, A.M.S. Vol.115, 2010.
 R. Fourer, D.M. Gay, B.W. Kernighan, Ampl: A Modeling Language for Mathematical Programming, Duxbury, 2002.
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.
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