Efficiency and Vectorial Optimization
Vasile Postolica
Citation : Vasile Postolica, Efficiency and Vectorial Optimization International Journal of Scientific and Innovative Mathematical Research 2018, 6(2) : 41-65.
This scientific research report was presented, in the quality of session chair and as an expert speech, at the 5th International Multi - Disciplinary Conference organized by Institute of Research Engineers and Doctors - IRED, USA September 02 - 03, 2017, Zurich, Switzerland. It is devoted to the general Efficiency presented inside the best appropriate environment of the infinite dimensional Ordered Vector Spaces, with its projections in Vectorial Optimization, that is, in Euclidean spaces Rn,n ∈ N* which can be extended, mutatis mutandis, to RI for every non -empty set I. Following our refined recent results, we especially use the largest class of the Convex Cones discovered till now in separated Locally Convex Spaces, named by us "Isac's Cones", and ensuring the existence together with important properties for the efficient points under completeness instead of compactness, with pertinent applications.The couched Open problems are generated by the new links between the General Efficiency, the Vector (Strong) Optimization and the Choquet Boundaries, since the Efficiency is strongly related to the General Optimization, the Potential Theory and conversely, with projections in the new recent and future fields of Scientific Research: Theory and Applications of the Generalized Dynamical Systems, Fixed points Theory, the Best Approximation Theory, the study of the Conically Bounded Sets, the study of the Nuclearity for the Topological Vector Spaces, Vector Optimization for multivalued functions and so on.