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A Note on Extended Characterization of Generalized Trade-Off Directions in Multiobjective Optimization




TekijätMäkelä MM, Nikulin Y, Mezei J

KustantajaHELDERMANN VERLAG

Julkaisuvuosi2012

JournalJournal of Convex Analysis

Tietokannassa oleva lehden nimiJOURNAL OF CONVEX ANALYSIS

Lehden akronyymiJ CONVEX ANAL

Numero sarjassa1

Vuosikerta19

Numero1

Aloitussivu91

Lopetussivu111

Sivujen määrä21

ISSN0944-6532


Tiivistelmä

We consider five basic optimality principles for a general multiobjective optimization problem with convex and nonconvex partial objectives. We introduce a generalization of the concept of trade-off directions defining them via some optimal surface of appropriate cones. In both cases, we link optimality and generalized trade-off directions by deriving geometrical optimality conditions in terms of appropriate cones. We scrutinize similarities and differences between the cases. Combining newly proven facts with some previously known results, we derive four general patterns reflecting structural properties and interconnections of the considered optimality principles. Additionally, we provide extended characterization of optimality for some peculiar cases.



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