Introducing oblique norms into multiple criteria programming (Q1598887)

Block norms, also referred as polyhedral norms, play an important role in the measurement of distance. In multiple criteria programming, norms have usually been used to identify the nondominated solutions that are the closest to some reference point. The definition of block norm and oblique norm as a specified block norm as well as two approaches to constructing oblique norm are given. In the paper the authors propose to use block norms to generate nondominated solutions of multiple criteria programs. The equivalence of finding the properly nondominated solutions of a mulliple criteria program and solving its scalarization by means of oblique norms is shown.