Connectedness and Stability of the Solution Sets in Linear Fractional Vector Optimization Problems
As it was shown by C. Malivert (1996) and other Authors, in a Linear Fractional Vector Optimization Problem (for short, LFVOP) any point satisfying the first-order necessary optimality condition (a stationary point) is a solution. Therefore, solving such a problem is equivalent to solve a monotone affine vector variational inequality of a special type. This observation allows us to apply the existing results on monotone affine variational inequality to establish some facts about connectedness and stability of the solution sets in LFVOP. In particular, we are able to solve a question raised by E. U. Choo and D. R. Atkins (1983) by proving that the set of all the efficient points (Pareto solutions) of a LFVOP with a bounded constraint set is connected.
Key WordsLinear fractional vector optimization monotone affine vector variational inequality solution set connectedness stability
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