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Multifacility Minimax Location Problems via Multi-Composed Optimization

机译：通过Multifacility极小极大位置问题Multi-Composed优化

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摘要

We present a conjugate duality approach for multifacility minimax location problems with geometric constraints, where the underlying space is Banach and the distances are measured by gauges of closed convex sets. Besides assigning corresponding conjugate dual problems, we derive necessary and sufficient optimality conditions. Moreover, we introduce a further dual problem with less dual variables than the first formulated dual and deliver corresponding statements of strong duality and optimality conditions. To illustrate the results of the latter duality approach and to give a more detailed characterization of the relation between the location problem and its dual, we consider the situation in the Euclidean space.
机译：我们提出一个共轭对偶方法multifacility极小极大位置的问题几何约束,底层空间巴拿赫和距离来衡量吗闭凸集的指标。相应的共轭对偶问题,我们得出必要且充分的最优性条件。此外,我们引入一个进一步的对偶问题用更少的双变量比第一双并交付相应的制定语句强劲的二元性和最优性条件。后者对偶方法和更多详细的描述之间的关系我们考虑的位置及其对偶问题,欧几里得空间的情况。

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