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Simplicially-Constrained DC Optimization over Efficient and Weakly Efficient Sets

Author

Listed:
  • H.A. Le Thi

    (National Institute for Applied Sciences—Rouen)

  • T. Pham Dinh

    (National Institute for Applied Sciences—Rouen)

  • L.D. Muu

    (Institute of Mathematics)

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.

Suggested Citation

  • H.A. Le Thi & T. Pham Dinh & L.D. Muu, 2003. "Simplicially-Constrained DC Optimization over Efficient and Weakly Efficient Sets," Journal of Optimization Theory and Applications, Springer, vol. 117(3), pages 503-531, June.
    • Handle: RePEc:spr:joptap:v:117:y:2003:i:3:d:10.1023_a:1023993504522
    DOI: 10.1023/A:1023993504522
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    References listed on IDEAS

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    2. R. Horst & N. V. Thoai, 1997. "Utility Function Programs and Optimization over the Efficient Set in Multiple-Objective Decision Making," Journal of Optimization Theory and Applications, Springer, vol. 92(3), pages 605-631, March.
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