Efficiency for a generalized form of vector optimization problems in complex space

Abstract

A generalized form of vector optimization problems in complex space is considered, where both the real and the imaginary parts of the objective functions are taken into account. The efficient solutions are defined and characterized in terms of optimal solutions of related appropriate scalar optimization problems. These scalar problems are formulated by means of vectors in the dual of the domination cone. Under analyticity hypotheses about the functions, complex extensions to necessary and sufficient conditions for efficiency of Kuhn–Tucker type are established. Most of the corresponding results of previous studies (in both finite-dimensional complex and real spaces) can be recovered as particular cases.

Keywords:

• vector optimization
• complex space
• efficient solutions
• scalarization
• optimality conditions

AMS Subject Classifications:

• 90C29
• 90C30
• 90C46

Notes

No potential conflict of interest was reported by the author.

Additional information

Funding

This work was supported by the King Faisal University, Saudi Arabia [grant number 110105].