Globally proper efficiency of set optimization problems based on the certainly set less order relation

Abstract

In this paper, we investigate the globally proper efficiency of set optimization problems. Firstly, we use the so-called certainly set less order relation to define a new kind of set order relation. Based on the new set order relation, we introduce the notion of the globally proper efficient solution of the set optimization problem. Secondly, we establish Lagrange multiplier rule of the set optimization problem. Finally, we obtain Lagrangian duality theorems and saddle point theorems. We also give some examples to illustrate our results.

Keywords:

• Set optimization
• globally proper efficient solution
• Lagrangian multiplier
• duality
• saddle point

AMS Subject Classifications:

• 90C26
• 90C29
• 90C30
• 90C46

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This research was supported by the National Nature Science Foundation of China (12171061 and 12071379), the Science and Technology Research Program of Chongqing Education Commission (KJZD-K202001104) and the Graduate Innovation Project of Chongqing (CYS21473).