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Simplicially-Constrained DC Optimization over Efficient and Weakly Efficient Sets

  • H.A. Le Thi
  • T. Pham Dinh
  • L.D. Muu
Article

Abstract

We formulate optimization problems over efficient and weakly efficient sets as DC problems over a simplex in the criteria space. This formulation allows developing a decomposition algorithm using an adaptive simplex subdivision and a convex envelope function for solving both problems. Randomly generated problems up to the size of 150 decision variables and 7 criteria are solved.

Optimization over efficient sets optimization over weakly efficient sets exact penalty functions DC programming simplicially-constrained DC optimization convex envelopes 

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Copyright information

© Plenum Publishing Corporation 2003

Authors and Affiliations

  • H.A. Le Thi
    • 1
  • T. Pham Dinh
    • 1
  • L.D. Muu
    • 2
  1. 1.Laboratory of Modelling, Optimization, and Operations ResearchNational Institute for Applied Sciences—RouenMont Saint AignanFrance
  2. 2.Institute of MathematicsHanoiVietnam

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