Global Optimization Approach to Optimizing Over the Efficient Set

  • Le Tu Luc
  • Le Dung Muu
Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 452)


We consider optimization problem over the efficient set of a linear vector problem where the objective function is a composite convex function of the criteria. We show that in this case the problem can be reduced to a single linear constrained convex maximization or a single convex-concave programming problem. The number of the “nonconvexity variables” in the both reduced forms is just equal to the number of the criteria. Some algoritmic aspects are discussed.

Key Words

Optimization over the Pareto set convex-concave programming convex maximization inner approximation decomposition 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Le Tu Luc
    • 1
  • Le Dung Muu
    • 2
  1. 1.RMITMelbourneAustralia
  2. 2.Institute of MathematicsHanoiVietnam

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