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DTSTART:20181028T030000
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DTSTART:20190331T020000
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UID:calendar.18153.field_data.0@www.diag.uniroma1.it
DTSTAMP:20240714T004147Z
CREATED:20190322T095959Z
DESCRIPTION:In multiobjective optimization\, one considers optimization pro
blems with several competing objective functions. For instance\, in engine
ering problems a design often has to be stable and light weighted at the s
ame time. A classical approach to such optimization problems is to formul
ate suitable parameter-dependent single-objective replacement problems\, c
alled scalarizations\, such as considering a weighted sum of the objective
functions. Then the parameters are varied and the scalarized problems are
solved iteratively. This talk is about numerical methods which do avoid
such scalarizations to improve the performance of the procedure.The first
algorithm which we present in this talk is for multiobjective optimization
problems with non-convex objective functions. Then\, methods of global
optimization are necessary to solve the replacement problems. Instead of t
his detour via scalarization\, we presents a direct deterministic method f
or finding a representation of all globally optimal solutions. This branch
-and-bound method is based on a subdivision of the feasible set and the co
nsideration of convex underestimators of the objective functions for the d
etermination of lower bounds.The second algorithm is for so called heterog
eneous multiobjective optimization problems\, i.e. problems\, where one of
the functions is assumed to be an expensive black-box function while the
other objectives are given analytically. The proposed method uses the basi
c trust region approach by restricting the computations in every iteration
to a local area. The objective functions are replaced by suitable models
which reflect the heterogeneity of the functions. Convergence results as w
ell as numerical experiments are presented.
DTSTART;TZID=Europe/Paris:20190325T100000
DTEND;TZID=Europe/Paris:20190325T100000
LAST-MODIFIED:20200515T073055Z
LOCATION:Aula A4 - DIAG
SUMMARY:Handling non-convex or expensive objectives: algorithms for multiob
jective optimization without scalarization - Prof. Gabriele Eichfelder
URL;TYPE=URI:http://www.diag.uniroma1.it/node/18153
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