A global approach to multiobjective optimization

ARGOMENTI: Seminars Ph.D. Program

Wednesday 13 May 2009 h. 15:00, room 2AB/40
Alberto LOVISON (Univ. Padova, Dip. Mat.)
"A global approach to multiobjective optimization"

In real life situations, there are usually more than one objective to deal with in order to design a successful project. For instance, a good car should be fast, while being low consuming as possible, should protect occupants while keeping compact external dimensions, should be comfortable and maximize, or minimize, at the same time, many other performance indicators.
Multiobjective optimization defines the mathematical framework for dealing with such problems. In this talk we propose a gentle introduction to this subject, strictly related to the standard single objective approach based on the study of critical points. We will recall the concept of Pareto critical set, introduced by Stephen Smale, and illustrate an effective algorithm for the global search of these critical sets. This topological approach allows the definition of a Morse theory for vector functions. On the other hand, severe restrictions derive from the curse of dimensionality and from the existence of structurally unstable singularities in higher dimensions.

Rif. int. C. Marastoni, T. Vargiolu, M. Dalla Riva

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