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Extended Characterization of Generalized Trade-Off Directions in Multiobjective Optimization

Marko M. Mäkelä, Yury Nikulin, Joszef Mezei, Extended Characterization of Generalized Trade-Off Directions in Multiobjective Optimization. TUCS Technical Reports 984, Turku Centre for Computer Science, 2010.

Abstract:

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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BibTeX entry:

@TECHREPORT{tMaNiMe10a,
  title = {Extended Characterization of Generalized Trade-Off Directions in Multiobjective Optimization},
  author = {Mäkelä, Marko M. and Nikulin, Yury and Mezei, Joszef},
  number = {984},
  series = {TUCS Technical Reports},
  publisher = {Turku Centre for Computer Science},
  year = {2010},
}

Belongs to TUCS Research Unit(s): Other

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