Optimality conditions for vector optimization problems with non-cone constraints in image space

ABSTRACT

In this paper, we employ the image space analysis method to investigate a vector optimization problem with non-cone constraints. First, we use the linear and nonlinear separation techniques to establish Lagrange-type sufficient and necessary optimality conditions of the given problem under convexity assumptions and generalized Slater condition. Moreover, we give some characterizations of generalized Lagrange saddle points in image space without any convexity assumptions. Finally, we derive the vectorial penalization for the vector optimization problem with non-cone constraints by a general way.

COMMUNICATED BY:

• Jen-Chih Yao

KEYWORDS:

• Nonlinear scalarization function
• separation function
• Lagrange-type optimality condition
• penalization

MATHEMATICS SUBJECT CLASSIFICATION 2010:

• 49K27
• 90C46

Acknowledgements

The authors are grateful to the referees for their valuable comments and suggestions, which helped to improve the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research was supported by the National Natural Science Foundation of China [grant numbers 11171362, 11571055].