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On Efficient Solutions to Multiple Objective Mathematical Programs

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Author Info

  • T. J. Lowe

    (Krannert Graduate School of Management, Purdue University, West Lafayette, Indiana 47907)

  • J.-F. Thisse

    (SPUR, Universite Catholique de Louvain, Louvain-la-Neuve, Belgium)

  • J. E. Ward

    (Krannert Graduate School of Management, Purdue University, West Lafayette, Indiana 47907)

  • R. E. Wendell

    (Graduate School of Business, University of Pittsburgh, Pittsburgh, Pennsylvania 15260)

Abstract

This note develops properties of quasi-efficient solutions and explores interrelationships to the classical concept of efficiency. In particular, a point is a quasi-efficient solution to a multiple objective mathematical program if and only if it is an optimal solution to a scalar maximum problem for some set of nonnegative weights on the objectives. This result is then used to characterize the set of quasi-efficient solutions as the union of efficient solutions to a multiple objective problem over all nonempty subsets of the objectives.

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File URL: http://dx.doi.org/10.1287/mnsc.30.11.1346
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Bibliographic Info

Article provided by INFORMS in its journal Management Science.

Volume (Year): 30 (1984)
Issue (Month): 11 (November)
Pages: 1346-1349

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Handle: RePEc:inm:ormnsc:v:30:y:1984:i:11:p:1346-1349

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Keywords: efficient solutions; mathematical programming; multiple objectives;

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Cited by:
  1. Nicolae Popovici & Matteo Rocca, 2010. "Pareto reducibility of vector variational inequalities," Economics and Quantitative Methods qf1004, Department of Economics, University of Insubria.

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