Characterization of properly optimal elements with variable ordering structures

In vector optimization with a variable ordering structure the partial ordering defined by a convex cone is replaced by a whole family of convex cones, one associated with each element of the space. In recent publications it was started to develop a comprehensive theory for these vector optimization problems. Thereby also notions of proper efficiency were generalized to variable ordering structures. In this paper we study the relation between several types of proper optimality. We give scalarization results based on new functionals defined by elements from the dual cones which allow characterizations also in the nonconvex case.


Optimization, Doi 10.1080/02331934.2015.1040793, 2015