A unified approach to Bishop-Phelps and scalarizing functionals

Abstract

. In this paper, functionals representing a negative convex cone as the solution set of an inequality are investigated. This general class of representing functionals includes various scalarizing functionals and Bishop-Phelps functionals. This unified approach extends some initial results to variable order structures, and additional properties of the representing functionals are given. The topics sublinearity, subdifferential, zeros, and separation are also treated in the context of representing functionals. Finally, the theory is applied to problems of vector and set optimization.