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ON THE PROJECTION OF THE EFFICIENT SET AND POTENTIAL APPLICATIONS

Abstract We study the efficient set X E for a multiple objective linear program by using its projection into the linear space L spanned by the independent criteria. We show that in the orthogonally complementary space of L, the efficient points form a polyhedron, while in L an efficiency-equivalent polyhedron for the projection P(X E ) of X E can be constructed by algorithms of outer and inner approximation types. These algorithms can be also used for generating all extreme points of P(X E ). Application to optimization over the efficient set for a multiple objective linear program is considered.