Global search perspectives for multiobjective optimization

Authors:
Alberto Lovison
Affiliations:
Dipartimento di Matematica, Università degli Studi di Padova, Padova, Italy 35121
Venue:
Journal of Global Optimization
Year:
2013

Citing 16
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Abstract

Extending the notion of global search to multiobjective optimization is far than straightforward, mainly for the reason that one almost always has to deal with infinite Pareto optima and correspondingly infinite optimal values. Adopting Stephen Smale's global analysis framework, we highlight the geometrical features of the set of Pareto optima and we are led to consistent notions of global convergence. We formulate then a multiobjective version of a celebrated result by Stephens and Baritompa, about the necessity of generating everywhere dense sample sequences, and describe a globally convergent algorithm in case the Lipschitz constant of the determinant of the Jacobian is known.