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Utility Function Programs and Optimization over the Efficient Set in Multiple-Objective Decision Making

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Abstract

Natural basic concepts in multiple-objective optimization lead to difficult multiextremal global optimization problems. Examples include detection of efficient points when nonconvexities occur, and optimization of a linear function over the efficient set in the convex (even linear) case. Assuming that a utility function exists allows one to replace in general the multiple-objective program by a single, nonconvex optimization problem, which amounts to a minimization over the efficient set when the utility function is increasing. A new algorithm is discussed for this utility function program which, under natural mild conditions, converges to an ∈-approximate global solution in a finite number of iterations. Applications include linear, convex, indefinite quadratic, Lipschitz, and d.c. objectives and constraints.

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Authors and Affiliations

  1. Fachbereich IV—Department of Mathematics, University of Trier, Trier, Germany

    R. Horst (Professor)

  2. Institute of Mathematics, Bo Ho, Hanoi, Vietnam;

    N. V. Thoai (Associate Professor)

  3. Fachbereich IV—Department of Mathematics, University of Trier, Trier, Germany

    N. V. Thoai (Associate Professor)

Authors
  1. R. Horst
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  2. N. V. Thoai
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Horst, R., Thoai, N.V. Utility Function Programs and Optimization over the Efficient Set in Multiple-Objective Decision Making. Journal of Optimization Theory and Applications 92, 605–631 (1997). https://doi.org/10.1023/A:1022659523991

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