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An Algorithm for Linearly-Constrained Piecewise Lexicographic Programming Problems

Author

Listed:
  • W. Ukovich

    (Universitá di Trieste)

  • S. Pastore

    (Universitá di Trieste)

  • A. Premoli

    (Politecnico di Milano)

Abstract

The linear piecewise lexicographic programming (LPWLGP) problem is a mathematical programming model with linear constraints and piecewise linear objective functions, arranged in a lexicographic hierarchy. Lexicographic spaces are introduced, and the differential properties of functions taking values in them are discussed. Necessary and sufficient optimality conditions for the LPWLGP problem are derived, and an algorithm based on them is formulated.

Suggested Citation

  • W. Ukovich & S. Pastore & A. Premoli, 2001. "An Algorithm for Linearly-Constrained Piecewise Lexicographic Programming Problems," Journal of Optimization Theory and Applications, Springer, vol. 111(1), pages 195-226, October.
    • Handle: RePEc:spr:joptap:v:111:y:2001:i:1:d:10.1023_a:1017583617249
    DOI: 10.1023/A:1017583617249
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    References listed on IDEAS

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    1. Ignizio, James P., 1985. "Multiobjective mathematical programming via the model and algorithm," European Journal of Operational Research, Elsevier, vol. 22(3), pages 338-346, December.
    2. James S. Dyer & Peter C. Fishburn & Ralph E. Steuer & Jyrki Wallenius & Stanley Zionts, 1992. "Multiple Criteria Decision Making, Multiattribute Utility Theory: The Next Ten Years," Management Science, INFORMS, vol. 38(5), pages 645-654, May.
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    Cited by:

    1. Soizic Adam & J. Bonnans & Ruben Paraisy & Sébastien Veyrat, 2011. "Application of convex lexicographical optimization to the balance of GRTgaz gas grid," Journal of Global Optimization, Springer, vol. 49(3), pages 415-423, March.

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