Theoretical Mathematics & Applications

Efficiency and Extensions in Infinite Dimensional Ordered Vector Spaces

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  • Abstract

    This research paper is focused on the common concepts of the efficiency and set-valued map. After a short introduction, we propose some questions regarding the notion of efficiency and we emphasize the Pareto optimality as one of the first finite dimensional illustrative examples. We present the efficiency and the multifunctions in the infinite dimensional ordered vector spaces following also our recent results concerning the most general concept of approximate efficiency, as a natural generalization of the efficiency, with implications and applications in vector optimization and the new links between the approximate efficiency, the strong optimization - by the full nuclear cones - and Choquet’s boundaries by an important coincidence result. In this way, the efficiency is strong related to the multifunctions and Potential theory through the agency of optimization and conversely. Significant examples of Isac’s cones and several pertinent references conclude this study.