Abstract
In this note, we consider the following multiple-objective linear program: maxCx, such thatAx=b,x≧0, and its associated Isermann dual program: minUb, such thatUAW≤Cw, for now≧0. We give a simple proof of the known fact that, for every dual efficient pointU°, there is a primal efficient pointx°, such thatU°b=Cx°. Parts of the ingredients in this proof are useful in exploring the structure of the dual feasible set of function values {Ub¦UAw≤Cw, for now≧0}.
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References
Isermann, H.,On Some Relations between a Dual Pair of Multiple Objective Programs, Zeitschrift für Operations Research, Vol. 22, pp. 33–41, 1978.
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Yu, P. L., andZeleny, M.,The Set of all Nondominated Solutions in Linear Cases and a Multicriteria Simplex Method, Journal of Mathematical Analysis and Applications, Vol. 49, pp. 430–468, 1975.
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Communicated by P. L. Yu
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Nieuwenhuis, J.W. About isermann duality. J Optim Theory Appl 41, 481–490 (1983). https://doi.org/10.1007/BF00935367
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DOI: https://doi.org/10.1007/BF00935367