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Generalizing Trade-Off Directions in Multiobjective Optimization

Marko Mäkelä, Yury Nikulin, Jozsef Mezei, Generalizing Trade-Off Directions in Multiobjective Optimization. Control and Cybernetics 3, 561 – 576, 2012.


We consider a general multiobjective optimization problem with five basic optimality
principles: efficiency, weak and proper Pareto optimality, strong efficiency and lexicographic optimality. We generalize the concept of trade-off directions defining them as some optimal surface of appropriate cones. In convex optimization, the contingent cone can be used for all optimality principles
except lexicographic optimality where the cone of feasible directions is useful. In nonconvex
case the contingent cone and the cone of locally feasible directions with lexicographic optimality are helpful. We derive necessary and sufficient geometrical optimality conditions in terms of corresponding trade-off directions for both convex and nonconvex cases.

BibTeX entry:

  title = {Generalizing Trade-Off Directions in Multiobjective Optimization},
  author = {Mäkelä, Marko and Nikulin, Yury and Mezei, Jozsef},
  journal = {Control and Cybernetics},
  volume = {3},
  pages = {561 – 576},
  year = {2012},
  keywords = {generalized trade-off directions, optimality principles, multiobjective optimization,},

Belongs to TUCS Research Unit(s): Turku Optimization Group (TOpGroup)

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