A Kind of Unified Strict Efficiency via Improvement Sets in Vector Optimization

In this paper, we propose a kind of unified strict efficiency named E-strict efficiency via improvement sets for vector optimization. This kind of efficiency is shown to be an extension of the classical strict efficiency and \(\varepsilon \)-strict efficiency and has many desirable properties. We also discuss some relationships with other properly efficiency based on improvement sets and establish the corresponding scalarization theorems by a base-functional and a nonlinear functional. Moreover, some examples are given to illustrate the main conclusions.