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Characterization of the solutions of multiobjective linear programming with a general dominated cone. (English) Zbl 0863.90123
Summary: We give a characterization of the solutions of a multiobjective linear programming problem with a general dominated cone. In such a problem the domination structure defined by the cone plays an important role. The dominated cone we adopt as the criterion in this paper is expressed in the form of a system of linear inequalities, but is not assumed to be acute. We first give a characterization theorem of the solutions, and next show, by the use of the theorem, that when the cone is not acute our problem can be transformed to another optimization problem with respect to a certain acute cone.

90C29 Multi-objective and goal programming
90C05 Linear programming