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A finite, nonadjacent extreme-point search algorithm for optimization over the efficient set

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Abstract

The problem (P) of optimizing a linear function over the efficient set of a multiple-objective linear program serves many useful purposes in multiple-criteria decision making. Mathematically, problem (P) can be classified as a global optimization problem. Such problems are much more difficult to solve than convex programming problems. In this paper, a nonadjacent extreme-point search algorithm is presented for finding a globally optimal solution for problem (P). The algorithm finds an exact extreme-point optimal solution for the problem after a finite number of iterations. It can be implemented using only linear programming methods. Convergence of the algorithm is proven, and a discussion is included of its main advantages and disadvantages.

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Authors and Affiliations

  1. College of Business Administration, University of Florida, Gainesville, Florida

    H. P. Benson (Professor)

Authors
  1. H. P. Benson
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Additional information

Communicated by P. L. Yu

The author owes thanks to two anonymous referees for their helpful comments.

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Benson, H.P. A finite, nonadjacent extreme-point search algorithm for optimization over the efficient set. J Optim Theory Appl 73, 47–64 (1992). https://doi.org/10.1007/BF00940077

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