6533b7d1fe1ef96bd125cbdb

RESEARCH PRODUCT

Sets of Efficiency in a Normed Space and Inner Product

Roland Durier

subject

Discrete mathematicsStrictly convex spaceConvex hullInner product spaceProduct (mathematics)Product topologyInverse problemMulti-objective optimizationNormed vector spaceMathematics

description

In a normed space X the distances to the points of a given set A being considered as the objective functions of a multicriteria optimization problem, we define four sets of efficiency (efficient, strictly efficient, weakly efficient and properly efficient points). Instead of studying properties of the sets of efficiency according to properties of the norm, we investigate an inverse problem: deduce properties of the norm of X from properties of the sets of efficiency, valid for every finite subset A of X.

yearjournalcountryeditionlanguage
1987-01-01
https://doi.org/10.1007/978-3-642-46618-2_6