Abstract
The concept of the well posedness for a special scalar problem is linked with strictly efficient solutions of vector optimization problem involving nearly convexlike set-valued maps. Two scalarization theorems and two Lagrange multiplier theorems for strict efficiency in vector optimization involving nearly convexlike set-valued maps are established. A dual is proposed and duality results are obtained in terms of strictly efficient solutions. A new type of saddle point, called strict saddle point, of an appropriate set-valued Lagrange map is introduced and is used to characterize strict efficiency.
Highlights
One important problem in vector optimization is to find the efficient points of a set
In this paper, we assume that C ⊂ Y and D ⊂ Z are pointed closed convex cone with nonempty interior
To show that (x, y) is a strictly efficient minimizer of (VP), for every ε > 0, we can let δ = inf{d−C(y − y) : ‖y − y‖ > ε}, and it implies that the proof is completed
Summary
One important problem in vector optimization is to find the efficient points of a set. Li [17] extended the concept of Benson proper efficiency to set-valued maps and presented two scalarization theorems and Lagrange multiplier theorems for set-valued vector optimization problem under cone subconvexlikeness. In this paper, inspired by [8, 17, 18], we study strict efficiency for vector optimization problem involving nearly cone-convexlike set-valued maps in the framework of real normed locally convex spaces.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
