Cone Characterizations of Approximate Solutions in Real-Vector Optimization

Borrowing concepts from linear algebra and convex analysis, it has been shown how the feasible set for a general vector optimization problem can be mapped under a linear transformation so that Pareto points in the image correspond to nondominated solutions for the original problem. The focus of this paper is to establish corresponding results for approximate nondominated points, based on a new characterization of these solutions using the concept of translated cones. The problem of optimizing over this set of approximate solutions is addressed and possible applications are given in the references.