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Radial Solutions and Orthogonal Trajectories in Multiobjective Global Optimization

Author

Listed:
  • A. Balbás

    (Universidad Carlos III)

  • E. Galperin

    (Université du Québec à Montréal)

  • P. Jiménez-Guerra

    (Universidad Nacional de Educación a Distancia)

Abstract

This paper presents a new, ray-oriented method for the global solution of nonscalarized vector optimization problems and a framework for the application of the Karush–Kuhn–Tucker theorem to such problems. Properties of nonlinear multiobjective problems implied by the Karush–Kuhn–Tucker necessary conditions are investigated. The regular case specific to nonscalarized MOPs is singled out when a nonlinear MOP with nonlinearities only in the constraints reduces to a nondegenerate linear system. It is shown that the trajectories of the Lagrange multipliers corresponding to the components of the vector cost function are orthogonal to the corresponding trajectories of the vector deviations in the balance space (to the balance set for Pareto solutions). Illustrative examples are presented.

Suggested Citation

  • A. Balbás & E. Galperin & P. Jiménez-Guerra, 2002. "Radial Solutions and Orthogonal Trajectories in Multiobjective Global Optimization," Journal of Optimization Theory and Applications, Springer, vol. 115(2), pages 315-344, November.
    • Handle: RePEc:spr:joptap:v:115:y:2002:i:2:d:10.1023_a:1020836221527
    DOI: 10.1023/A:1020836221527
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    References listed on IDEAS

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    1. E. A. Galperin, 1997. "Pareto Analysis vis-à-vis Balance Space Approach in Multiobjective Global Optimization," Journal of Optimization Theory and Applications, Springer, vol. 93(3), pages 533-545, June.
    2. E. Galperin & P. Jimenez Guerra, 2001. "Duality of Nonscalarized Multiobjective Linear Programs: Dual Balance, Level Sets, and Dual Clusters of Optimal Vectors," Journal of Optimization Theory and Applications, Springer, vol. 108(1), pages 109-137, January.
    3. M. Ehrgott & H. W. Hamacher & K. Klamroth & S. Nickel & A. Schöbel & M. M. Wiecek, 1997. "Equivalence of Balance Points and Pareto Solutions in Multiple-Objective Programming," Journal of Optimization Theory and Applications, Springer, vol. 92(1), pages 209-212, January.
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