Approximate Proper Eciency for Multiobjective Optimization Problems

Abstract

This paper is devoted to the study of a new kind of approximate properly efficiency
in terms of proximal normal cone and co-radiant set for multiobjective optimization problem. We
derive some properties of the new approximate proper  efficiency and discuss the relations with
the existing approximate concepts, such as approximate efficiency, approximate Benson proper
 efficiency and approximate Borwein proper  efficiency. At last, we study the linear scalarizations
for the new approximate proper  efficiency under the generalized convexity assumptions and give
some examples to illustrate the main results.